Electric field due to continuous charge distribution
•Download as PPTX, PDF•
15 likes•6,072 views
This document discusses how to calculate the electric field due to continuous distributions of charge. It explains that charges can be modeled as continuously distributed along a line, over a surface, or throughout a volume. The electric field is then calculated through an integral performed over the entire charge distribution.
Report
Share
Report
Share
Recommended
Electric field intensity
This document summarizes key concepts related to electric fields. It defines electric fields and their relationship to force. It then describes the electric field intensity and field patterns due to various charge distributions including point charges, multiple charges, infinite line charges, and infinite surface charges. It also covers Gauss's law relating electric field and charge distribution.
Gauss's Law & its Applications
These slides describe Gauss's Law in electrostatics and its application to find out electric field due to point charge, uniformly charged spherical shell, and electric potential due to spherical shell.
Visit this link: https://phystudypoint.blogspot.com
GUASS LAW
Gauss's law relates the electric flux through a closed surface to the electric charge enclosed by the surface. It can be used to calculate the electric field due to various charge distributions like:
- A point charge, where the electric field is spherically symmetric and directed radially outward.
- An infinite line charge, where the electric field is directed radially outward and its magnitude depends only on the distance from the wire.
- An infinite plane sheet, where the electric field is uniform and perpendicular to the sheet.
- Two parallel charged sheets, where the electric field is zero outside and uniform inside, directed from the positive to negative sheet.
- A charged spherical shell, where the electric field
Gauss's Law and its applications
This document discusses the application of Gauss's law to calculate electric field intensity in two situations:
1) Inside a hollow metallic sphere with charge distributed over its surface. Using Gauss's law, the electric field inside the sphere is found to be zero, showing how electric force can be shielded.
2) Near an infinite sheet with uniform surface charge density. A Gaussian cylinder is used to calculate the flux, yielding an electric field intensity of σ/(2ε0) perpendicular to the sheet. Gauss's law allows calculating electric fields for complex charge distributions.
COULOMB'S LAW
1) Charles Augustine de Coulomb published his law in 1785 stating that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
2) He used a torsion balance to measure the attractive and repulsive forces between charged objects and determine that the magnitude of the force depends on the medium between the charges.
3) Coulomb's law can be used to calculate the force between two charges, as well as the electric field and applications include calculating force or distance between charges and the force on a point from multiple charges using the superposition principle.
Maxwell's equation
Maxwell's equations describe the relationship between electric and magnetic fields. Gauss' law states that the divergence of the electric flux density equals the electric charge density. Gauss' magnetism law states that the divergence of the magnetic flux density is always zero. Faraday's law describes how a changing magnetic field generates an electric field. Ampere's law shows the relationship between electric current and the surrounding magnetic field. Maxwell unified electricity, magnetism, and light through his equations, which can be written in differential or integral form and describe fields in free space or harmonically varying fields.
Gauss’s Law
Gauss's law can be used to determine electric field strength around symmetrical charge distributions. It states that the electric flux through a closed surface is proportional to the enclosed charge. The electric field is zero inside conductors because excess charge resides entirely on the surface and electrons move freely to cancel out any internal field. Common applications include finding the field of a point charge, conducting sphere, or charged sheet.
Poynting vector
The Poynting vector S is defined as the cross product of the electric field E and magnetic field H, and represents the direction of power flow per unit area. It has units of watts per square meter. Maxwell's equations relate the Poynting vector to energy storage and dissipation within a volume. For a coaxial cable carrying a steady current I with a voltage V between conductors, the power flow along the cable equals the product of the voltage and current.
Recommended
Electric field intensity
This document summarizes key concepts related to electric fields. It defines electric fields and their relationship to force. It then describes the electric field intensity and field patterns due to various charge distributions including point charges, multiple charges, infinite line charges, and infinite surface charges. It also covers Gauss's law relating electric field and charge distribution.
Gauss's Law & its Applications
These slides describe Gauss's Law in electrostatics and its application to find out electric field due to point charge, uniformly charged spherical shell, and electric potential due to spherical shell.
Visit this link: https://phystudypoint.blogspot.com
GUASS LAW
Gauss's law relates the electric flux through a closed surface to the electric charge enclosed by the surface. It can be used to calculate the electric field due to various charge distributions like:
- A point charge, where the electric field is spherically symmetric and directed radially outward.
- An infinite line charge, where the electric field is directed radially outward and its magnitude depends only on the distance from the wire.
- An infinite plane sheet, where the electric field is uniform and perpendicular to the sheet.
- Two parallel charged sheets, where the electric field is zero outside and uniform inside, directed from the positive to negative sheet.
- A charged spherical shell, where the electric field
Gauss's Law and its applications
This document discusses the application of Gauss's law to calculate electric field intensity in two situations:
1) Inside a hollow metallic sphere with charge distributed over its surface. Using Gauss's law, the electric field inside the sphere is found to be zero, showing how electric force can be shielded.
2) Near an infinite sheet with uniform surface charge density. A Gaussian cylinder is used to calculate the flux, yielding an electric field intensity of σ/(2ε0) perpendicular to the sheet. Gauss's law allows calculating electric fields for complex charge distributions.
COULOMB'S LAW
1) Charles Augustine de Coulomb published his law in 1785 stating that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
2) He used a torsion balance to measure the attractive and repulsive forces between charged objects and determine that the magnitude of the force depends on the medium between the charges.
3) Coulomb's law can be used to calculate the force between two charges, as well as the electric field and applications include calculating force or distance between charges and the force on a point from multiple charges using the superposition principle.
Maxwell's equation
Maxwell's equations describe the relationship between electric and magnetic fields. Gauss' law states that the divergence of the electric flux density equals the electric charge density. Gauss' magnetism law states that the divergence of the magnetic flux density is always zero. Faraday's law describes how a changing magnetic field generates an electric field. Ampere's law shows the relationship between electric current and the surrounding magnetic field. Maxwell unified electricity, magnetism, and light through his equations, which can be written in differential or integral form and describe fields in free space or harmonically varying fields.
Gauss’s Law
Gauss's law can be used to determine electric field strength around symmetrical charge distributions. It states that the electric flux through a closed surface is proportional to the enclosed charge. The electric field is zero inside conductors because excess charge resides entirely on the surface and electrons move freely to cancel out any internal field. Common applications include finding the field of a point charge, conducting sphere, or charged sheet.
Poynting vector
The Poynting vector S is defined as the cross product of the electric field E and magnetic field H, and represents the direction of power flow per unit area. It has units of watts per square meter. Maxwell's equations relate the Poynting vector to energy storage and dissipation within a volume. For a coaxial cable carrying a steady current I with a voltage V between conductors, the power flow along the cable equals the product of the voltage and current.
ELECTROSTATIC POTENTIAL ENERGY
1. Electrostatic potential is defined as the work done per unit charge to bring a test charge from infinity to a point in an electric field.
2. The electric potential at a point due to a single point charge is directly proportional to the charge and inversely proportional to the distance from the charge.
3. The electric potential at a point due to multiple charges is equal to the sum of the potentials due to each individual charge.
Maxwell's equations 3rd 2
Maxwell's equations describe the fundamental interactions between electricity and magnetism. They include:
1) Gauss's law for electric fields, which relates the electric flux through a closed surface to the electric charge enclosed.
2) Gauss's law for magnetic fields, which states that the magnetic flux through a closed surface is always zero, since there are no magnetic monopoles.
3) Faraday's law, which describes how a changing magnetic field induces an electric field. It relates the circulating electric field to the rate of change of the magnetic field.
4) The Ampere-Maxwell law, which describes how electric currents and changing electric fields generate magnetic fields. It relates the magnetic field to the electric current
Ampere's law
(1) Ampere's Circuital Law relates the net magnetic field along a closed loop to the electric current passing through the loop. It was first discovered by André-Marie Ampère in 1826.
(2) The law states that the line integral of the magnetic field over a closed path equals the permeability of free space times the total current enclosed by that closed loop. It can be expressed mathematically as an integral or differential equation.
(3) Applications of the law include calculating the magnetic field inside and outside a long cylindrical conductor, finding the magnetic field of a solenoid, and determining the magnetic field of a toroidal solenoid.
Electric Charge and Electric Field Lecture
More: http://www.pinoybix.org
Lesson Objectives:
Static Electricity; Electric Charge and Its Conservation
Electric Charge in the Atom
Insulators and Conductors
Induced Charge; the Electroscope
Coulomb’s Law
Solving Problems Involving Coulomb’s Law and Vectors
The Electric Field
Field Lines
Electric Fields and Conductors
Gauss’s Law
Electric Forces in Molecular Biology: DNA Structure and Replication
Photocopy Machines and Computer Printers Use Electrostatics
Electrostatics Class 12- Part 2
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole moment, and the electric field intensity and torque experienced by dipoles.
Electric flux (2)
Gauss's law states that the electric flux through any closed surface is equal to 1/ε0 times the total charge enclosed by the surface. The document then explains Gauss's law and the Gaussian surface method for calculating electric field intensity. It provides an example of using Gauss's law to find that the electric field intensity inside a hollow charged sphere is zero since there is no enclosed charge.
current¤t density
The document summarizes key concepts related to electric current, current density, and magnetostatics. It defines:
- Electric current as the rate of charge transfer through a surface. The SI unit is the ampere.
- Conventional current direction versus actual electron flow direction in conductors.
- Current density as the current per unit area, with units of amperes per square meter. It is proportional to and in the same direction as the electric field in a conductor based on Ohm's law.
- Surface and volume current density and how they relate to the Biot-Savart law for calculating magnetic fields.
Electric Field
1. A field is defined as a property of space in which a material object experiences a force. For example, above the earth there is a gravitational field where a mass experiences a downward force.
2. The electric field is a vector field that exists around an electric charge even when no other charges are present. The direction of the electric field points away from a positive charge and towards a negative charge.
3. The electric field strength is defined as the force experienced by a hypothetical positive test charge per unit of charge, located at that point in space.
Electric Potential
The document discusses electric field, potential, and energy. It defines electric potential as the work done to move a unit positive charge from infinity to a point in an electric field. Electric potential is a scalar quantity measured in volts. Equipotentials are regions in space where the electric potential has a constant value, forming equipotential surfaces or lines. Analogies are drawn between electric and gravitational fields, such as both following inverse square laws and having field lines and equipotentials.
Electric Fields
The document discusses electric fields and electrostatics. It explains that when objects are rubbed together, electrons are transferred causing objects to become charged. It then discusses Coulomb's law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It provides equations for calculating electric field strength, potential, and force experienced by charges in fields.
Magnetostatics (1)
1) Magnetostatic fields are produced when charges move with constant velocity, originating from currents like those in wires.
2) Biot-Savart's law describes the magnetic field produced by a current element, with the field proportional to the current and inversely proportional to the distance.
3) Ampere's law, in integral and differential form, relates the line integral of the magnetic field around a closed path to the total current passing through the enclosed surface.
Electrostatics
This document provides a summary of Lecture 2 on electrostatics. It introduces fundamental concepts such as electric charge, Coulomb's law, electric field, electric potential, and the relationship between electric field and electric potential. Continuous distributions of charge such as volume, surface, and line charges are also discussed. Key equations for calculating electric fields and potentials from these various charge distributions are presented.
Faradays law
basic principles of electrical machines,faraday's laws of electro magnetic induction principle.dynamically induced Emf statically induced emf applications to electrical machines
Ampere's circuital law and its applications
Let's consider a bar of magnetic material (iron) placed in a uniform magnetic field of strength H. Ampere's law relates the net magnetic field along a closed loop to the electric current passing through the loop. It states that the integral of the magnetic field density B around any closed path is equal to the current enclosed by the path multiplied by the permeability of the medium. Ampere's law has various applications such as determining the magnetic field around a long, straight current-carrying wire.
5 slides
This document discusses plane electromagnetic waves. It defines plane waves as waves whose wavefronts are infinite parallel planes of constant amplitude normal to the phase velocity vector. The electric and magnetic fields of a plane wave are perpendicular to each other and to the direction of propagation. Plane waves can be linearly, circularly, or elliptically polarized depending on the orientation and behavior of the electric field vector over time. Linear polarization occurs when the electric field is oriented along a fixed line. Circular polarization results when the electric field traces out a circle, and elliptical polarization is characterized by an elliptical trace.
Fundamental Concepts on Electromagnetic Theory
The document summarizes key concepts from a presentation on electromagnetic theory. It discusses different types of fields, including scalar and vector fields. It also covers gradient, divergence, curl, coordinate systems, static electric and magnetic fields, Maxwell's equations, and other fundamental electromagnetic concepts. Multiple students contributed sections on topics including Coulomb's law, Biot-Savart law, Lorentz force, and Maxwell's equations in differential, integral and harmonic forms.
Electromagnetic Induction Class 12
1. Electromagnetic induction occurs when a changing magnetic flux induces an electromotive force (emf) in a circuit. This was discovered by Faraday through his experiments.
2. Faraday's laws of induction state that an emf is induced in a circuit when the magnetic flux through the circuit changes, and that the magnitude of this induced emf is proportional to the rate of change of the magnetic flux.
3. Lenz's law describes the direction of the induced current: the current will flow in a direction that creates its own magnetic field to oppose the original change in magnetic flux that caused it. This ensures the conservation of energy.
gauss law and application Arun kumar
This document provides an overview of Gauss's law and its applications. It begins with definitions of electric flux and how to calculate flux through surfaces. It then introduces Gauss's law, which relates the electric flux through a closed surface to the enclosed charge. Examples are provided to demonstrate how to use Gauss's law to determine electric fields for symmetric charge distributions. The document also discusses how the electric field is zero inside conductors in electrostatic equilibrium and how Gauss's law can be used to show this. Worked examples further illustrate applying Gauss's law.
2180 phys lect 3
1. The document discusses electric flux and Gauss's law. Electric flux is defined as the product of the electric field and the perpendicular surface area. Gauss's law states that the total electric flux through a closed surface is proportional to the enclosed charge.
2. Examples are presented for applying Gauss's law to calculate electric fields produced by spherically symmetric charge distributions like a point charge or thin spherical shell, as well as a cylindrically symmetric charged rod. The calculations involve setting up Gaussian surfaces and relating the flux to the enclosed charge.
3. Key results are that the electric field of a point charge follows an inverse square law, a thin spherical shell produces no field inside but an inverse square field outside, and the
Probability Problems
This document provides a tutorial on probability problems with examples and solutions. It contains two questions:
1) A coin is tossed 1000 times with 499 heads and 501 tails. The empirical probability of heads is 0.499 and tails is 0.501. The sum of the two probabilities equals 1.
2) In a cricket match, a batswoman hits a boundary 6 times out of 30 balls. The probability that she did not hit a boundary is calculated as 24/30 = 4/5.
The document explains how to calculate empirical probabilities from sample data and find the probability of complementary events. It provides the full worked out solutions and explanations.
What is probability
This document provides an overview of key concepts in probability. It defines probability as a measure of likelihood between 0 and 1, and discusses how probability is used in various fields. Key terms are explained, such as randomness, trial, independent trial, experiment, event, and sample space. Randomness refers to experiments with unpredictable outcomes, like rolling a die. Trials are the individual occurrences of an experiment, like each coin toss. The document also discusses empirical probability, which is the probability of an event calculated based on the frequency of outcomes from experiments. Empirical probability depends on the specific experiment and can take on different values.
More Related Content
What's hot
ELECTROSTATIC POTENTIAL ENERGY
1. Electrostatic potential is defined as the work done per unit charge to bring a test charge from infinity to a point in an electric field.
2. The electric potential at a point due to a single point charge is directly proportional to the charge and inversely proportional to the distance from the charge.
3. The electric potential at a point due to multiple charges is equal to the sum of the potentials due to each individual charge.
Maxwell's equations 3rd 2
Maxwell's equations describe the fundamental interactions between electricity and magnetism. They include:
1) Gauss's law for electric fields, which relates the electric flux through a closed surface to the electric charge enclosed.
2) Gauss's law for magnetic fields, which states that the magnetic flux through a closed surface is always zero, since there are no magnetic monopoles.
3) Faraday's law, which describes how a changing magnetic field induces an electric field. It relates the circulating electric field to the rate of change of the magnetic field.
4) The Ampere-Maxwell law, which describes how electric currents and changing electric fields generate magnetic fields. It relates the magnetic field to the electric current
Ampere's law
(1) Ampere's Circuital Law relates the net magnetic field along a closed loop to the electric current passing through the loop. It was first discovered by André-Marie Ampère in 1826.
(2) The law states that the line integral of the magnetic field over a closed path equals the permeability of free space times the total current enclosed by that closed loop. It can be expressed mathematically as an integral or differential equation.
(3) Applications of the law include calculating the magnetic field inside and outside a long cylindrical conductor, finding the magnetic field of a solenoid, and determining the magnetic field of a toroidal solenoid.
Electric Charge and Electric Field Lecture
More: http://www.pinoybix.org
Lesson Objectives:
Static Electricity; Electric Charge and Its Conservation
Electric Charge in the Atom
Insulators and Conductors
Induced Charge; the Electroscope
Coulomb’s Law
Solving Problems Involving Coulomb’s Law and Vectors
The Electric Field
Field Lines
Electric Fields and Conductors
Gauss’s Law
Electric Forces in Molecular Biology: DNA Structure and Replication
Photocopy Machines and Computer Printers Use Electrostatics
Electrostatics Class 12- Part 2
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole moment, and the electric field intensity and torque experienced by dipoles.
Electric flux (2)
Gauss's law states that the electric flux through any closed surface is equal to 1/ε0 times the total charge enclosed by the surface. The document then explains Gauss's law and the Gaussian surface method for calculating electric field intensity. It provides an example of using Gauss's law to find that the electric field intensity inside a hollow charged sphere is zero since there is no enclosed charge.
current¤t density
The document summarizes key concepts related to electric current, current density, and magnetostatics. It defines:
- Electric current as the rate of charge transfer through a surface. The SI unit is the ampere.
- Conventional current direction versus actual electron flow direction in conductors.
- Current density as the current per unit area, with units of amperes per square meter. It is proportional to and in the same direction as the electric field in a conductor based on Ohm's law.
- Surface and volume current density and how they relate to the Biot-Savart law for calculating magnetic fields.
Electric Field
1. A field is defined as a property of space in which a material object experiences a force. For example, above the earth there is a gravitational field where a mass experiences a downward force.
2. The electric field is a vector field that exists around an electric charge even when no other charges are present. The direction of the electric field points away from a positive charge and towards a negative charge.
3. The electric field strength is defined as the force experienced by a hypothetical positive test charge per unit of charge, located at that point in space.
Electric Potential
The document discusses electric field, potential, and energy. It defines electric potential as the work done to move a unit positive charge from infinity to a point in an electric field. Electric potential is a scalar quantity measured in volts. Equipotentials are regions in space where the electric potential has a constant value, forming equipotential surfaces or lines. Analogies are drawn between electric and gravitational fields, such as both following inverse square laws and having field lines and equipotentials.
Electric Fields
The document discusses electric fields and electrostatics. It explains that when objects are rubbed together, electrons are transferred causing objects to become charged. It then discusses Coulomb's law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It provides equations for calculating electric field strength, potential, and force experienced by charges in fields.
Magnetostatics (1)
1) Magnetostatic fields are produced when charges move with constant velocity, originating from currents like those in wires.
2) Biot-Savart's law describes the magnetic field produced by a current element, with the field proportional to the current and inversely proportional to the distance.
3) Ampere's law, in integral and differential form, relates the line integral of the magnetic field around a closed path to the total current passing through the enclosed surface.
Electrostatics
This document provides a summary of Lecture 2 on electrostatics. It introduces fundamental concepts such as electric charge, Coulomb's law, electric field, electric potential, and the relationship between electric field and electric potential. Continuous distributions of charge such as volume, surface, and line charges are also discussed. Key equations for calculating electric fields and potentials from these various charge distributions are presented.
Faradays law
basic principles of electrical machines,faraday's laws of electro magnetic induction principle.dynamically induced Emf statically induced emf applications to electrical machines
Ampere's circuital law and its applications
Let's consider a bar of magnetic material (iron) placed in a uniform magnetic field of strength H. Ampere's law relates the net magnetic field along a closed loop to the electric current passing through the loop. It states that the integral of the magnetic field density B around any closed path is equal to the current enclosed by the path multiplied by the permeability of the medium. Ampere's law has various applications such as determining the magnetic field around a long, straight current-carrying wire.
5 slides
This document discusses plane electromagnetic waves. It defines plane waves as waves whose wavefronts are infinite parallel planes of constant amplitude normal to the phase velocity vector. The electric and magnetic fields of a plane wave are perpendicular to each other and to the direction of propagation. Plane waves can be linearly, circularly, or elliptically polarized depending on the orientation and behavior of the electric field vector over time. Linear polarization occurs when the electric field is oriented along a fixed line. Circular polarization results when the electric field traces out a circle, and elliptical polarization is characterized by an elliptical trace.
Fundamental Concepts on Electromagnetic Theory
The document summarizes key concepts from a presentation on electromagnetic theory. It discusses different types of fields, including scalar and vector fields. It also covers gradient, divergence, curl, coordinate systems, static electric and magnetic fields, Maxwell's equations, and other fundamental electromagnetic concepts. Multiple students contributed sections on topics including Coulomb's law, Biot-Savart law, Lorentz force, and Maxwell's equations in differential, integral and harmonic forms.
Electromagnetic Induction Class 12
1. Electromagnetic induction occurs when a changing magnetic flux induces an electromotive force (emf) in a circuit. This was discovered by Faraday through his experiments.
2. Faraday's laws of induction state that an emf is induced in a circuit when the magnetic flux through the circuit changes, and that the magnitude of this induced emf is proportional to the rate of change of the magnetic flux.
3. Lenz's law describes the direction of the induced current: the current will flow in a direction that creates its own magnetic field to oppose the original change in magnetic flux that caused it. This ensures the conservation of energy.
gauss law and application Arun kumar
This document provides an overview of Gauss's law and its applications. It begins with definitions of electric flux and how to calculate flux through surfaces. It then introduces Gauss's law, which relates the electric flux through a closed surface to the enclosed charge. Examples are provided to demonstrate how to use Gauss's law to determine electric fields for symmetric charge distributions. The document also discusses how the electric field is zero inside conductors in electrostatic equilibrium and how Gauss's law can be used to show this. Worked examples further illustrate applying Gauss's law.
2180 phys lect 3
1. The document discusses electric flux and Gauss's law. Electric flux is defined as the product of the electric field and the perpendicular surface area. Gauss's law states that the total electric flux through a closed surface is proportional to the enclosed charge.
2. Examples are presented for applying Gauss's law to calculate electric fields produced by spherically symmetric charge distributions like a point charge or thin spherical shell, as well as a cylindrically symmetric charged rod. The calculations involve setting up Gaussian surfaces and relating the flux to the enclosed charge.
3. Key results are that the electric field of a point charge follows an inverse square law, a thin spherical shell produces no field inside but an inverse square field outside, and the
What's hot (20)
More from physicscatalyst
Probability Problems
This document provides a tutorial on probability problems with examples and solutions. It contains two questions:
1) A coin is tossed 1000 times with 499 heads and 501 tails. The empirical probability of heads is 0.499 and tails is 0.501. The sum of the two probabilities equals 1.
2) In a cricket match, a batswoman hits a boundary 6 times out of 30 balls. The probability that she did not hit a boundary is calculated as 24/30 = 4/5.
The document explains how to calculate empirical probabilities from sample data and find the probability of complementary events. It provides the full worked out solutions and explanations.
What is probability
This document provides an overview of key concepts in probability. It defines probability as a measure of likelihood between 0 and 1, and discusses how probability is used in various fields. Key terms are explained, such as randomness, trial, independent trial, experiment, event, and sample space. Randomness refers to experiments with unpredictable outcomes, like rolling a die. Trials are the individual occurrences of an experiment, like each coin toss. The document also discusses empirical probability, which is the probability of an event calculated based on the frequency of outcomes from experiments. Empirical probability depends on the specific experiment and can take on different values.
Series and parallel arrangement of capacitors
This document discusses capacitors connected in parallel and series circuits. When capacitors are in parallel, the equivalent capacitance is the sum of the individual capacitances and the voltage is the same across each capacitor. When capacitors are in series, the equivalent capacitance is calculated by taking the reciprocal of the sum of the reciprocals of the individual capacitances and the charge is the same across each capacitor. An example problem is worked out where three equal-valued capacitors are connected in a combination of parallel and series connections to find the equivalent capacitance of the overall circuit and the charge on one of the capacitors.
What are Polynomials
This document provides an overview of polynomials. It defines polynomials as expressions with multiple terms where the exponents are whole numbers. Monomials have one term, binomials have two terms, and trinomials have three terms. Polynomials can have variables, constants, and exponents of whole numbers. Expressions with non-whole number exponents or fractions are not polynomials. The document also notes that polynomials of one variable can be written as a sum of terms with coefficients and descending exponents, and the highest exponent indicates the degree of the polynomial.
How to solve rational numbers problems
This document provides solutions to two problems about finding rational numbers between given values. For the first problem, it finds the three rational numbers between 1 and 2 using an average method and a number line method. For the second problem, it finds the three rational numbers between 1/3 and 7/2 again using an average method and a method of converting the fractions to a common denominator. The document explains each step of the solutions in detail.
What are rational numbers
Rational numbers can be expressed as fractions p/q where p and q are integers and q is not zero. All integers, natural numbers, and whole numbers are rational numbers. There are an infinite number of rational numbers between any two rational numbers. Rational numbers either terminate as decimals or repeat as non-terminating decimals. The sum, difference, product, and quotient of rational numbers are also rational numbers, meaning rational numbers are closed under the operations of addition, subtraction, multiplication, and division.
How to solve momentum problems
This document provides instructions on how to solve momentum problems in physics. It defines momentum as mass times velocity (p=mv) and explains that the total momentum of a system is equal to the vector sum of the momentum of objects within it. It also states that the change in momentum of an object is equal to the applied force times the time over which it acts (p2-p1=Ft). The document then works through an example problem involving calculating the average force and final momentum of a golf ball hit by a club to demonstrate how to apply these momentum equations.
How to solve center of mass Problems
The document discusses the concept of center of mass and how to solve center of mass problems. It defines center of mass as the point where the total mass of a system can be considered to be concentrated. The velocity and acceleration of the center of mass can be calculated using the formulas provided. In the absence of external forces, the velocity of the center of mass remains constant. Examples are provided to demonstrate how to calculate the position of the center of mass for a system of particles and how the center of mass will continue along the original path after a rocket explodes into parts due to no change in external forces.
Parallel Plate capacitor
1) Capacitance is a measure of the ability of a system to store electric charge. It consists of two non-touching plates that store equal but opposite charges.
2) The capacitance C of a system is defined as the ratio of the stored charge Q to the potential difference V between the plates.
3) For a parallel plate capacitor, the capacitance is given by C=ε0A/d, where ε0 is the permittivity of free space, A is the area of each plate, and d is the distance between the plates.
Thermodynamics processes in physics
The document discusses the first law of thermodynamics and different thermodynamic processes. The first law states that the energy put into a system equals the sum of the work done by the system and the change in internal energy. An isothermal process occurs at constant temperature, with heat equal to work. An adiabatic process involves no heat transfer, so a change in internal energy is equal and opposite to work, causing temperature to increase or decrease depending on the work's direction.
Moment of inertia concepts in Rotational Mechanics
Moment of inertia is a measure of an object's resistance to changes in its angular acceleration due to an applied torque. It depends on how the object's mass is distributed relative to its pivot point. The moment of inertia of a rigid body can be calculated by imagining it divided into particles, multiplying each particle's mass by the square of its distance from the axis of rotation, and summing these values. Important theorems for calculating moment of inertia include the perpendicular axis theorem and parallel axis theorem. Examples are given for calculating the moment of inertia of a solid disk and sphere about their central axes.
How to Solve the Force Problems
This document provides instructions for solving force problems in physics:
1. Draw a diagram showing all forces and choose a coordinate system.
2. Make free body diagrams for each object showing all forces.
3. Resolve all forces into components using the coordinate system and apply Newton's Second Law.
4. Identify known and unknown values and solve the equations, ensuring the same number of equations as unknowns. Check units.
It then works through an example problem involving three connected objects to find accelerations and contact forces. The example solves the problem by drawing free body diagrams, applying Newton's Second Law to each object, and combining the equations.
Free body diagram Concept in Mechanics
A free body diagram is a sketch that shows an isolated body and all the external forces acting on it. It does not show internal forces or the body's environment. Forces are drawn as vectors at the point where they are applied. Common forces shown include weight, normal force, friction, and tension. Free body diagrams are used to write force balance equations for mechanical systems. Examples of free body diagrams include a block on a ramp, a book on a table, an object in projectile motion, and an object slowing down due to friction.
How can you apply Gauss's Law
This document discusses how to apply Gauss's law to find the electric field through a surface. It explains that Gauss's law can be used when the distribution of electric charge inside the surface and the electric field through the surface are known. The document also notes that the Gaussian surface should be selected based on the symmetry of the charge distribution, such as a cylindrical surface for an infinitely long line of uniform charge.
Apply Gauss's law to find electric field due to linear distribution of charges
Gauss's law can be used to find the electric field due to a long, straight wire with a uniform charge distribution. At points far from the ends of the wire, the electric field lines will be radial and perpendicular to the wire. The electric field only depends on the linear charge density and not on the length of the wire.
Derivation of Coulomb law from Gauss's Law
Gauss's law can be used to derive Coulomb's law, which describes the electrostatic force between two point charges. An isolated positive charge will produce a radial electric field of equal magnitude at all points the same distance r from the charge. Taking advantage of the symmetry, Gauss's law relates the electric flux through a Gaussian surface enclosing the charge to the enclosed charge, allowing the derivation of the inverse square relationship in Coulomb's law.
Gausslaw
Gauss's law relates the electric flux through a closed surface to the net electric charge enclosed by the surface. It states that the total electric flux through any closed surface is equal to 1/ε0 times the net charge enclosed, divided by the permittivity of free space ε0. Gauss's law provides an easier way to calculate electric fields than Coulomb's law and can be used to find electric fields when you know the charge distribution inside the surface.
More from physicscatalyst (17)
Moment of inertia concepts in Rotational Mechanics
Moment of inertia concepts in Rotational Mechanics
Apply Gauss's law to find electric field due to linear distribution of charges
Apply Gauss's law to find electric field due to linear distribution of charges
Recently uploaded
The Diamonds of 2023-2024 in the IGRA collection
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
Hindi varnamala | hindi alphabet PPT.pdf
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
clinical examination of hip joint (1).pdf
described clinical examination all orthopeadic conditions .
How to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
Community pharmacy- Social and preventive pharmacy UNIT 5
Covered community pharmacy topic of the subject Social and preventive pharmacy for Diploma and Bachelor of pharmacy
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Digital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments Unit - NGV Pavilion Concept Design
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Main Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Recently uploaded (20)
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
Community pharmacy- Social and preventive pharmacy UNIT 5
Community pharmacy- Social and preventive pharmacy UNIT 5
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Electric field due to continuous charge distribution
- 1. Electric field due to continuous charge distributions
- 2. Charges on surface of system are located very close together and can be assumed to have continuous distribution of charges. In a system of closely spaced charges charge could be continuously distributed along Some line Over a surface Throughout a volume
- 3. A
- 4. This integral is done over the entire charge distribution.
- 5. Line Charge