- The Biot-Savart law describes the magnetic field generated by a steady current-carrying conductor. It states that the magnetic field dB at a point P is proportional to the current I, the length of the conductor element ds, and inversely proportional to the distance r between the element and the point.
- For a straight, infinite wire, the total magnetic field B at a distance a from the wire is proportional to the current I and inversely proportional to the distance a.
- For conductors of finite length, the total magnetic field B is calculated by integrating the contribution of the magnetic field dB from each element ds of the conductor.
The document discusses magnetic fields produced by electric currents. It begins by introducing the Biot-Savart law, which describes how a current-carrying element contributes to the magnetic field at a point. It then provides an example of using the law to calculate the magnetic field at the center of a circular arc carrying a current. Finally, it describes magnetic field lines and how to determine the direction of the magnetic field using the right-hand rule.
1) Magnets attract iron-containing materials due to their magnetic properties which arise from the alignment of electron spins in their atoms.
2) Øersted discovered that electric currents produce magnetic fields according to the right-hand rule. Biot-Savart's law describes how the magnetic field is produced by a current-carrying conductor.
3) Biot-Savart's law states that the magnetic field produced by a current element is directly proportional to the current and length of the element and inversely proportional to the distance from the element. The direction of the magnetic field is perpendicular to both the current element and the line from the element to the point of interest.
Magnetic Effects Of Current Class 12 Part-1Self-employed
The document discusses the magnetic effects of electric current, including:
1) Oersted's experiment showing a current-carrying wire deflects a magnetic needle.
2) Rules for determining the direction of magnetic fields, including Ampere's swimming rule and Maxwell's corkscrew rule.
3) Biot-Savart's law, which describes the magnetic field created by a current-carrying element as proportional to the current and inversely proportional to the distance.
The document discusses the magnetic effects of electric current. It describes Oersted's experiment which showed that a current-carrying wire deflects a nearby compass needle. It then provides rules for determining the direction of magnetic fields, including Ampere's swimming rule and the right hand thumb rule. Biot-Savart's law is introduced, relating the magnetic field to properties of the current. Magnetic field calculations are shown for a straight wire, circular loop, and solenoid carrying current.
The document discusses the magnetic effects of electric current. It begins by describing Oersted's experiment which showed a magnetic needle deflecting when placed near a current-carrying wire. It then provides rules for determining the direction of magnetic fields, including Ampere's swimming rule and the right hand thumb rule. Biot-Savart's law is introduced, stating the magnetic field is proportional to the current and inversely proportional to the distance squared. Magnetic field calculations are shown for a straight wire, circular loop, and solenoid carrying current.
The document discusses the magnetic effects of electric current, including:
1) Oersted's experiment showing a current-carrying wire deflects a magnetic needle.
2) Rules for determining the direction of magnetic fields, including Ampere's swimming rule and Maxwell's corkscrew rule.
3) Biot-Savart's law relating the magnetic field to the current, length element, and distance.
4) Expressions for the magnetic field of an infinitely long straight wire, circular loop, and solenoid.
The document discusses the magnetic effects of electric current. It begins by explaining Oersted's experiment which showed that electric current produces a magnetic field. It then provides several rules for determining the direction of magnetic fields, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right hand thumb rule. Biot-Savart's law is introduced to quantify the magnetic field produced by a current-carrying element. Expressions are derived for the magnetic fields produced by an infinitely long straight wire, a circular loop, and a solenoid.
The Biot-Savart law describes the magnetic field generated by electric currents. It states that the magnetic field at a point P due to a current element I ds is proportional to the current I and inversely proportional to the distance r from the current element to the point P. The field is also proportional to the length of the current element ds and perpendicular to both r and ds. Integrating this contribution from all current elements gives the total magnetic field generated by the current distribution. Specific applications include calculating the field from a long straight wire, circular loop, and tightly wound coil.
The document discusses magnetic fields produced by electric currents. It begins by introducing the Biot-Savart law, which describes how a current-carrying element contributes to the magnetic field at a point. It then provides an example of using the law to calculate the magnetic field at the center of a circular arc carrying a current. Finally, it describes magnetic field lines and how to determine the direction of the magnetic field using the right-hand rule.
1) Magnets attract iron-containing materials due to their magnetic properties which arise from the alignment of electron spins in their atoms.
2) Øersted discovered that electric currents produce magnetic fields according to the right-hand rule. Biot-Savart's law describes how the magnetic field is produced by a current-carrying conductor.
3) Biot-Savart's law states that the magnetic field produced by a current element is directly proportional to the current and length of the element and inversely proportional to the distance from the element. The direction of the magnetic field is perpendicular to both the current element and the line from the element to the point of interest.
Magnetic Effects Of Current Class 12 Part-1Self-employed
The document discusses the magnetic effects of electric current, including:
1) Oersted's experiment showing a current-carrying wire deflects a magnetic needle.
2) Rules for determining the direction of magnetic fields, including Ampere's swimming rule and Maxwell's corkscrew rule.
3) Biot-Savart's law, which describes the magnetic field created by a current-carrying element as proportional to the current and inversely proportional to the distance.
The document discusses the magnetic effects of electric current. It describes Oersted's experiment which showed that a current-carrying wire deflects a nearby compass needle. It then provides rules for determining the direction of magnetic fields, including Ampere's swimming rule and the right hand thumb rule. Biot-Savart's law is introduced, relating the magnetic field to properties of the current. Magnetic field calculations are shown for a straight wire, circular loop, and solenoid carrying current.
The document discusses the magnetic effects of electric current. It begins by describing Oersted's experiment which showed a magnetic needle deflecting when placed near a current-carrying wire. It then provides rules for determining the direction of magnetic fields, including Ampere's swimming rule and the right hand thumb rule. Biot-Savart's law is introduced, stating the magnetic field is proportional to the current and inversely proportional to the distance squared. Magnetic field calculations are shown for a straight wire, circular loop, and solenoid carrying current.
The document discusses the magnetic effects of electric current, including:
1) Oersted's experiment showing a current-carrying wire deflects a magnetic needle.
2) Rules for determining the direction of magnetic fields, including Ampere's swimming rule and Maxwell's corkscrew rule.
3) Biot-Savart's law relating the magnetic field to the current, length element, and distance.
4) Expressions for the magnetic field of an infinitely long straight wire, circular loop, and solenoid.
The document discusses the magnetic effects of electric current. It begins by explaining Oersted's experiment which showed that electric current produces a magnetic field. It then provides several rules for determining the direction of magnetic fields, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right hand thumb rule. Biot-Savart's law is introduced to quantify the magnetic field produced by a current-carrying element. Expressions are derived for the magnetic fields produced by an infinitely long straight wire, a circular loop, and a solenoid.
The Biot-Savart law describes the magnetic field generated by electric currents. It states that the magnetic field at a point P due to a current element I ds is proportional to the current I and inversely proportional to the distance r from the current element to the point P. The field is also proportional to the length of the current element ds and perpendicular to both r and ds. Integrating this contribution from all current elements gives the total magnetic field generated by the current distribution. Specific applications include calculating the field from a long straight wire, circular loop, and tightly wound coil.
The Biot-Savart law describes the magnetic field generated by electric current. It relates the magnetic field strength to characteristics of the current such as its magnitude, direction, length, and distance from the field point. The law states that the magnetic field is proportional to the current and inversely proportional to the distance from it. It is analogous to Coulomb's law for electrostatics and is fundamental to magnetostatics. Examples of applying the law include calculating the magnetic field of a straight wire or circular loop of current.
magnetic effect of current class 12th physics pptArpit Meena
1) Oersted's experiment showed that an electric current produces a magnetic field, as a compass needle was deflected when placed near a current-carrying wire.
2) There are several rules to determine the direction of magnetic fields, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right-hand thumb rule.
3) Biot-Savart's law quantitatively describes the magnetic field generated by a current-carrying conductor in terms of the current, length of conductor, and distance from the field point. It shows the field depends on the sine of the angle between the current and field point.
The document discusses the magnetic effects of electric current, including Oersted's experiment showing a magnetic needle deflecting near a current-carrying wire. It introduces several rules for determining the direction of magnetic fields, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right-hand thumb rule. Biot-Savart's law is presented relating the magnetic field to the current, length element, distance, and angle. Magnetic field calculations are shown for a straight wire, circular loop, and solenoid carrying current.
The Biot-Savart law describes the magnetic field generated by electric currents. It states that the magnetic field at a point P is proportional to the current I and inversely proportional to the distance r from the current element ds. Specifically, the field is given by the equation dB = (μ0I/4πr2)ds x r̂, where μ0 is the permeability of free space. This law can be used to calculate the magnetic fields generated by various current distributions like long straight wires, circular loops, and coils.
This document summarizes key concepts from a chapter on magnetic fields. It discusses the magnetic field created by a current-carrying wire, which is perpendicular to the wire. It also describes how a current loop acts as a magnet, with a magnetic dipole moment proportional to the current and area of the loop. Additionally, it covers Ampere's law relating the line integral of magnetic field around a closed loop to the current passing through the enclosed area.
- The document discusses magnetic fields created by electric currents. It covers the magnetic field of a moving point charge, the Biot-Savart law for calculating the magnetic field from a current-carrying wire, and an example calculation of the magnetic field from a long straight wire.
- The right hand rule is introduced for determining the direction of magnetic fields.
- Maxwell's equations for static magnetic fields in integral and differential form are presented.
- The document discusses magnetic fields created by electric currents. It covers the magnetic field of a moving point charge, the Biot-Savart law for calculating the magnetic field from a current-carrying wire, and an example calculation of the magnetic field from a long straight wire.
- The right hand rule is introduced for determining the direction of magnetic fields.
- Maxwell's equations for static magnetic fields in integral and differential form are presented.
This document discusses the Biot-Savart law and its use in calculating magnetic fields. It begins by describing Biot and Savart's experimental observations which led to the mathematical expression of the Biot-Savart law. It then provides examples of using the law to calculate the magnetic field of a circular current loop and an ideal solenoid. For the solenoid, Ampere's law is used to derive an expression showing the interior magnetic field is directly proportional to the current and number of turns per unit length.
The document discusses magnetic fields produced by electric currents. It begins by introducing the Biot-Savart law, which describes the magnetic field generated by a straight wire carrying a current. It then examines the magnetic field of a circular current loop, noting that the field depends on the current I, distance R from the loop, and radius a. At large distances R compared to the radius a, the field approximates that of a magnetic dipole with a magnetic dipole moment m proportional to the current I and area A of the loop.
1) When an electric current flows through a wire, it produces a magnetic field around the wire. Oersted discovered this through an experiment where a magnetic needle deflected when placed near a current-carrying wire.
2) Several rules describe the direction of magnetic fields produced by currents, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right-hand thumb rule.
3) Biot-Savart's law quantitatively relates the magnetic field to the current, length, and position. It shows the field depends on the current and is inversely proportional to the distance from the wire.
This document discusses the magnetic effects of electric current. It begins by describing Oersted's experiment which discovered that electric currents produce magnetic fields. It then provides several rules for determining the direction of magnetic fields, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right hand thumb rule. The document continues by defining the Lorentz magnetic force law and Fleming's left hand rule. It also discusses the magnetic fields produced by various current configurations including infinite straight conductors, circular loops, and solenoids using Biot-Savart's law.
1) Ampere's circuital law states that the line integral of the magnetic field B around any closed path is equal to the permeability of free space times the total current passing through the enclosed area.
2) The law can be used to calculate magnetic fields due to various current carrying conductors like long straight wires, solenoids, and toroids.
3) For a long straight wire, the magnetic field at a distance r is given by B=μ0I/2πr. For a solenoid, the magnetic field inside is uniform and given by B=μ0nI, where n is number of turns per unit length. For a toroid, the magnetic field within is also
This document provides an introduction to diodes and pn junctions. It discusses the basic diode characteristics including their ability to act as switches that allow current flow in one direction but not the other. It then covers energy band diagrams of pn junctions, showing how the bands bend at equilibrium and under applied biases. Key points are made about the built-in voltage and electric field created. The document also describes how current flows in the forward and reverse bias conditions based on the band diagrams. Finally, it provides an overview of tunnel diodes and their unique I-V characteristics enabled by quantum tunneling.
1) The Biot-Savart law describes the magnetic field generated by a current-carrying conductor. It states that the magnetic field is proportional to the current and inversely proportional to the distance from the current element.
2) The direction of the magnetic field generated by a current element is perpendicular to both the current element and the line from the current element to the point where the magnetic field is calculated.
3) Examples of applying the Biot-Savart law include calculating the magnetic field generated by a circular loop of wire and along the axis of a solenoid. The magnetic fields add linearly for multiple current elements.
This document discusses key concepts in vector calculus including paths, surfaces, volumes, and three important theorems - the gradient theorem, divergence theorem, and curl theorem. It defines paths, surfaces, and volumes and explains that they can be scalar or vector quantities depending on whether they represent lengths, areas, or volumes. It also introduces the concepts of differential length, area, and volume and expresses them mathematically in Cartesian, cylindrical and spherical coordinate systems. Finally, it states the mathematical formulations of the three theorems - the gradient theorem relates a line integral to function values, the divergence theorem relates a volume integral to a surface integral, and the curl theorem relates a surface integral to a closed line integral.
- Ampere's Law relates the magnetic field B to the enclosed current. It is the magnetic analogue of Coulomb's Law.
- The magnetic vector potential A is defined such that B is equal to the curl of A, allowing magnetic fields to be represented without reference to a scalar potential.
- Relative permeability describes how the magnetic field B is modified by the presence of a magnetic material, in analogy to how relative permittivity modifies the electric field E.
1) The document discusses different types of PN junction devices including PN junction diodes, rectifiers, LEDs, laser diodes, and Zener diodes.
2) It explains the structure and operation of PN junction diodes, describing how a PN junction is formed and how diffusion causes a depletion region and barrier potential.
3) The characteristics of PN junction diodes under forward and reverse bias are discussed, including their V-I characteristics and the factors that determine diode current.
This document discusses kinematics of particles using polar components. It defines the position vector of a particle as the vector from the origin to the particle's position. For curvilinear motion, the instantaneous velocity vector is defined as the limit of the displacement vector divided by the time interval as the interval approaches zero. Similarly, the instantaneous acceleration vector is defined as the limit of the change in velocity vector over the time interval. Polar components (radial and transverse) and tangential and normal components are also introduced to analyze curvilinear motion. Expressions are derived for velocity and acceleration in terms of these component directions. An example problem of a centrifuge is worked out using these concepts.
This document defines key terms related to circles such as diameter, radius, secant, chord, and tangent. It provides theorems about lines that are tangent to a circle, including that a tangent line is perpendicular to the radius drawn at the point of tangency. The document also includes examples of using these properties to solve for variables in geometric figures where segments are tangent to a circle.
The document discusses the magnetic effects of electric current. It begins by describing Oersted's experiment which showed that electric current produces a magnetic field. It then provides several rules for determining the direction of magnetic fields, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right hand thumb rule. The document goes on to define Biot-Savart's law and describes how to use it to calculate magnetic fields produced by straight wires, circular loops of wire, and solenoids. It also discusses the magnetic force on a current-carrying conductor and the torque experienced by a current-carrying coil in a uniform magnetic field.
The document summarizes Newton's law of gravitation and Kepler's laws of planetary motion. It provides equations and examples to explain how gravity works based on the inverse square law and how planetary orbits can be modeled. It also discusses how Cavendish calculated G, the gravitational constant, and how early astronomers like Copernicus, Brahe, Galileo and Kepler contributed to the development of our understanding of gravity and planetary motion.
This document provides information about nuclear physics and nuclear structure. It defines fundamental nuclear particles like protons, neutrons and electrons. It describes atomic structure, including the nucleus and isotopes. It discusses nuclear properties such as mass defect and binding energy. It also covers radioactive decay processes like alpha, beta, and gamma emission. Key concepts are defined, such as half-life, activity, and nuclear reactions. Examples are provided to demonstrate calculations involving these nuclear physics concepts.
The Biot-Savart law describes the magnetic field generated by electric current. It relates the magnetic field strength to characteristics of the current such as its magnitude, direction, length, and distance from the field point. The law states that the magnetic field is proportional to the current and inversely proportional to the distance from it. It is analogous to Coulomb's law for electrostatics and is fundamental to magnetostatics. Examples of applying the law include calculating the magnetic field of a straight wire or circular loop of current.
magnetic effect of current class 12th physics pptArpit Meena
1) Oersted's experiment showed that an electric current produces a magnetic field, as a compass needle was deflected when placed near a current-carrying wire.
2) There are several rules to determine the direction of magnetic fields, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right-hand thumb rule.
3) Biot-Savart's law quantitatively describes the magnetic field generated by a current-carrying conductor in terms of the current, length of conductor, and distance from the field point. It shows the field depends on the sine of the angle between the current and field point.
The document discusses the magnetic effects of electric current, including Oersted's experiment showing a magnetic needle deflecting near a current-carrying wire. It introduces several rules for determining the direction of magnetic fields, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right-hand thumb rule. Biot-Savart's law is presented relating the magnetic field to the current, length element, distance, and angle. Magnetic field calculations are shown for a straight wire, circular loop, and solenoid carrying current.
The Biot-Savart law describes the magnetic field generated by electric currents. It states that the magnetic field at a point P is proportional to the current I and inversely proportional to the distance r from the current element ds. Specifically, the field is given by the equation dB = (μ0I/4πr2)ds x r̂, where μ0 is the permeability of free space. This law can be used to calculate the magnetic fields generated by various current distributions like long straight wires, circular loops, and coils.
This document summarizes key concepts from a chapter on magnetic fields. It discusses the magnetic field created by a current-carrying wire, which is perpendicular to the wire. It also describes how a current loop acts as a magnet, with a magnetic dipole moment proportional to the current and area of the loop. Additionally, it covers Ampere's law relating the line integral of magnetic field around a closed loop to the current passing through the enclosed area.
- The document discusses magnetic fields created by electric currents. It covers the magnetic field of a moving point charge, the Biot-Savart law for calculating the magnetic field from a current-carrying wire, and an example calculation of the magnetic field from a long straight wire.
- The right hand rule is introduced for determining the direction of magnetic fields.
- Maxwell's equations for static magnetic fields in integral and differential form are presented.
- The document discusses magnetic fields created by electric currents. It covers the magnetic field of a moving point charge, the Biot-Savart law for calculating the magnetic field from a current-carrying wire, and an example calculation of the magnetic field from a long straight wire.
- The right hand rule is introduced for determining the direction of magnetic fields.
- Maxwell's equations for static magnetic fields in integral and differential form are presented.
This document discusses the Biot-Savart law and its use in calculating magnetic fields. It begins by describing Biot and Savart's experimental observations which led to the mathematical expression of the Biot-Savart law. It then provides examples of using the law to calculate the magnetic field of a circular current loop and an ideal solenoid. For the solenoid, Ampere's law is used to derive an expression showing the interior magnetic field is directly proportional to the current and number of turns per unit length.
The document discusses magnetic fields produced by electric currents. It begins by introducing the Biot-Savart law, which describes the magnetic field generated by a straight wire carrying a current. It then examines the magnetic field of a circular current loop, noting that the field depends on the current I, distance R from the loop, and radius a. At large distances R compared to the radius a, the field approximates that of a magnetic dipole with a magnetic dipole moment m proportional to the current I and area A of the loop.
1) When an electric current flows through a wire, it produces a magnetic field around the wire. Oersted discovered this through an experiment where a magnetic needle deflected when placed near a current-carrying wire.
2) Several rules describe the direction of magnetic fields produced by currents, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right-hand thumb rule.
3) Biot-Savart's law quantitatively relates the magnetic field to the current, length, and position. It shows the field depends on the current and is inversely proportional to the distance from the wire.
This document discusses the magnetic effects of electric current. It begins by describing Oersted's experiment which discovered that electric currents produce magnetic fields. It then provides several rules for determining the direction of magnetic fields, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right hand thumb rule. The document continues by defining the Lorentz magnetic force law and Fleming's left hand rule. It also discusses the magnetic fields produced by various current configurations including infinite straight conductors, circular loops, and solenoids using Biot-Savart's law.
1) Ampere's circuital law states that the line integral of the magnetic field B around any closed path is equal to the permeability of free space times the total current passing through the enclosed area.
2) The law can be used to calculate magnetic fields due to various current carrying conductors like long straight wires, solenoids, and toroids.
3) For a long straight wire, the magnetic field at a distance r is given by B=μ0I/2πr. For a solenoid, the magnetic field inside is uniform and given by B=μ0nI, where n is number of turns per unit length. For a toroid, the magnetic field within is also
This document provides an introduction to diodes and pn junctions. It discusses the basic diode characteristics including their ability to act as switches that allow current flow in one direction but not the other. It then covers energy band diagrams of pn junctions, showing how the bands bend at equilibrium and under applied biases. Key points are made about the built-in voltage and electric field created. The document also describes how current flows in the forward and reverse bias conditions based on the band diagrams. Finally, it provides an overview of tunnel diodes and their unique I-V characteristics enabled by quantum tunneling.
1) The Biot-Savart law describes the magnetic field generated by a current-carrying conductor. It states that the magnetic field is proportional to the current and inversely proportional to the distance from the current element.
2) The direction of the magnetic field generated by a current element is perpendicular to both the current element and the line from the current element to the point where the magnetic field is calculated.
3) Examples of applying the Biot-Savart law include calculating the magnetic field generated by a circular loop of wire and along the axis of a solenoid. The magnetic fields add linearly for multiple current elements.
This document discusses key concepts in vector calculus including paths, surfaces, volumes, and three important theorems - the gradient theorem, divergence theorem, and curl theorem. It defines paths, surfaces, and volumes and explains that they can be scalar or vector quantities depending on whether they represent lengths, areas, or volumes. It also introduces the concepts of differential length, area, and volume and expresses them mathematically in Cartesian, cylindrical and spherical coordinate systems. Finally, it states the mathematical formulations of the three theorems - the gradient theorem relates a line integral to function values, the divergence theorem relates a volume integral to a surface integral, and the curl theorem relates a surface integral to a closed line integral.
- Ampere's Law relates the magnetic field B to the enclosed current. It is the magnetic analogue of Coulomb's Law.
- The magnetic vector potential A is defined such that B is equal to the curl of A, allowing magnetic fields to be represented without reference to a scalar potential.
- Relative permeability describes how the magnetic field B is modified by the presence of a magnetic material, in analogy to how relative permittivity modifies the electric field E.
1) The document discusses different types of PN junction devices including PN junction diodes, rectifiers, LEDs, laser diodes, and Zener diodes.
2) It explains the structure and operation of PN junction diodes, describing how a PN junction is formed and how diffusion causes a depletion region and barrier potential.
3) The characteristics of PN junction diodes under forward and reverse bias are discussed, including their V-I characteristics and the factors that determine diode current.
This document discusses kinematics of particles using polar components. It defines the position vector of a particle as the vector from the origin to the particle's position. For curvilinear motion, the instantaneous velocity vector is defined as the limit of the displacement vector divided by the time interval as the interval approaches zero. Similarly, the instantaneous acceleration vector is defined as the limit of the change in velocity vector over the time interval. Polar components (radial and transverse) and tangential and normal components are also introduced to analyze curvilinear motion. Expressions are derived for velocity and acceleration in terms of these component directions. An example problem of a centrifuge is worked out using these concepts.
This document defines key terms related to circles such as diameter, radius, secant, chord, and tangent. It provides theorems about lines that are tangent to a circle, including that a tangent line is perpendicular to the radius drawn at the point of tangency. The document also includes examples of using these properties to solve for variables in geometric figures where segments are tangent to a circle.
The document discusses the magnetic effects of electric current. It begins by describing Oersted's experiment which showed that electric current produces a magnetic field. It then provides several rules for determining the direction of magnetic fields, including Ampere's swimming rule, Maxwell's corkscrew rule, and the right hand thumb rule. The document goes on to define Biot-Savart's law and describes how to use it to calculate magnetic fields produced by straight wires, circular loops of wire, and solenoids. It also discusses the magnetic force on a current-carrying conductor and the torque experienced by a current-carrying coil in a uniform magnetic field.
The document summarizes Newton's law of gravitation and Kepler's laws of planetary motion. It provides equations and examples to explain how gravity works based on the inverse square law and how planetary orbits can be modeled. It also discusses how Cavendish calculated G, the gravitational constant, and how early astronomers like Copernicus, Brahe, Galileo and Kepler contributed to the development of our understanding of gravity and planetary motion.
This document provides information about nuclear physics and nuclear structure. It defines fundamental nuclear particles like protons, neutrons and electrons. It describes atomic structure, including the nucleus and isotopes. It discusses nuclear properties such as mass defect and binding energy. It also covers radioactive decay processes like alpha, beta, and gamma emission. Key concepts are defined, such as half-life, activity, and nuclear reactions. Examples are provided to demonstrate calculations involving these nuclear physics concepts.
The document defines key concepts in elasticity including stress, strain, elastic limit, plasticity, rigidity. It describes three types of stress (tensile, volume, shear) and three types of strain (longitudinal, volume, shear). It introduces three elastic constants: Young's modulus, bulk modulus, and modulus of rigidity. Young's modulus is the ratio of tensile stress to longitudinal strain. Bulk modulus is the ratio of volume stress to volume strain. Modulus of rigidity is the ratio of shear stress to shear strain. Poisson's ratio is defined as the ratio of lateral strain to longitudinal strain.
This document discusses adiabatic relations between pressure, volume, and temperature from the Department of Physics at Shri Govindrao Munghate Arts and Science College in Kurkheda. The head of the physics department, Prof. B.V. Tupte, focuses on adiabatic processes and the relationships between these thermodynamic variables.
This document discusses the Carnot cycle and the second law of thermodynamics. It defines a heat engine and describes the key components of the Carnot cycle, including the isothermal and adiabatic processes. It explains that the Carnot cycle is reversible and defines the maximum possible efficiency for converting heat into work. The document concludes by stating the Kelvin-Planck and Clausius formulations of the second law - that it is impossible to convert all heat from a single body into work or to spontaneously transfer heat from a cold to hot body.
The document discusses the second law of thermodynamics. It begins by describing some limitations of the first law, such as not predicting whether processes are possible or specifying direction. It then defines the second law as "heat cannot flow itself from a colder body to a hotter body." The second law introduces the concept of entropy as a measure of system disorder. It also helps determine the preferred direction of processes and states that entropy always increases for irreversible processes in closed systems. The document provides examples of reversible and irreversible processes.
Work done During an adiabatic Process.pptxBhaskarTupte2
This document discusses work done during an adiabatic process. It defines an adiabatic process as one where no heat is exchanged between a system and its surroundings. The document states that for an adiabatic expansion, work is done by the system so its internal energy decreases, while for an adiabatic compression, work is done on the system so its internal energy increases. It also explains that the work done in an adiabatic process depends only on the initial and final temperatures of the system.
This document discusses work done during an isothermal process. An isothermal process is defined as one where the temperature of the system remains constant. Heat can flow from the system to the surroundings and vice versa in order to keep the temperature constant. For ideal gases, if the change in temperature is zero, the change in internal energy is also zero, so the heat transferred equals the work done.
The document discusses the Zeroth law of thermodynamics. It states that if two systems, A and B, are each in thermal equilibrium with a third system C, then A and B must also be in thermal equilibrium with each other. Thermal equilibrium refers to equality of temperatures between systems, meaning all three systems - A, B, and C - will be at the same temperature. The Zeroth law provides a basis for comparing temperatures between different systems.
This document discusses different thermodynamic processes. It defines a thermodynamic process as a chemical or physical process that changes a system from an initial state to a final state. It then describes four main types of thermodynamic processes: isolated, closed, open, isothermal, isochoric, isobaric, and adiabatic. For each process, it provides the key characteristics, such as whether the system can exchange energy and mass with its surroundings.
The document discusses the second law of thermodynamics. It begins by describing some limitations of the first law, such as not predicting whether processes are possible or specifying direction. It then defines the second law as "heat cannot flow itself from a colder body to a hotter body." The second law introduces the concept of entropy as a measure of system disorder. It also helps determine the preferred direction of processes and states that entropy always increases for irreversible processes in closed systems. The document provides examples of reversible and irreversible processes.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
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
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it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
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1. Shri Govindrao Munghate Arts and Science
College , Kurkheda
Department of Physics
Topic –The Biot-Savart Law
Prof. B.V. Tupte
Head, Department of Physics
Shri Govindrao Munghate Arts and Science
College Kurkheda.
2. • Biot and Savart recognized that a conductor
carrying a steady current produces a force on a
magnet.
• Biot and Savart produced an equation that gives
the magnetic field at some point in space in
terms of the current that produces the field.
• Biot-Savart law says that if a wire carries a steady
current I, the magnetic field dB at some point P
associated with an element of conductor length
ds has the following properties:
– The vector dB is perpendicular to both ds (the
direction of the current I) and to the unit
vector rhat directed from the element ds to the
point P.
3.
4. – The magnitude of dB is inversely
proportional to r2, where r is the
distance from the element ds to the
point P.
– The magnitude of dB is proportional
to the current I and to the length ds
of the element.
– The magnitude of dB is proportional
to sin q, where q is the angle
between the vectors ds and rhat.
• Biot-Savart law:
2
o
r
π
4
r̂
x
ds
I
μ
dB
5. • mo is a constant called the permeability of
free space; mo =4· x 10-7 Wb/A·m (T·m/A)
• Biot-Savart law gives the magnetic field at a
point for only a small element of the
conductor ds.
• To determine the total magnetic field B at
some point due to a conductor of specified
size, we must add up every contribution
from all elements ds that make up the
conductor (integrate)!
2
o
r
r̂
x
ds
π
4
I
μ
dB
6. • The direction of the magnetic field
due to a current carrying element
is perpendicular to both the
current element ds and the radius
vector rhat.
• The right hand rule can be used to
determine the direction of the
magnetic field around the current
carrying conductor:
– Thumb of the right hand in the
direction of the current.
– Fingers of the right hand curl around
the wire in the direction of the
magnetic field at that point.
7. Magnetic Field of a Thin Straight
Conductor
• Consider a thin, straight wire
carrying a constant current I
along the x axis. To determine
the total magnetic field B at the
point P at a distance a from the
wire:
8. • Use the right hand rule to determine that
the direction of the magnetic field
produced by the conductor at point P is
directed out of the page.
• This is also verified using the vector cross
product (ds x rhat): fingers of right hand in
direction of ds; point palm in direction of
rhat (curl fingers from ds to rhat); thumb
points in direction of magnetic field B.
• The cross product (ds x rhat) = ds·rhat·sin q;
rhat is a unit vector and the magnitude of a
unit vector = 1.
• (ds x rhat) = ds·rhat·sin q ds·sin q
9. • Each length of the conductor ds is also a small
length along the x axis, dx.
• Each element of length ds is a distance r from P
and a distance x from the midpoint of the
conductor O. The angle q will also change as r and
x change.
• The values for r, x, and q will change for each
different element of length ds.
• Let ds = dx, then ds·sin q becomes dx·sin q.
• The contribution to the total magnetic field at
point P from each element of the conductor ds is:
2
o
r
θ
sin
dx
π
4
I
μ
dB
10. • The total magnetic field B at point P can be
determined by integrating from one end of
the conductor to the other end of the
conductor.
• The distance a from the midpoint of the
conductor O to the point P remains
constant.
• Express r in terms of a and x.
• Express sin q in terms of a and r.
2
1
2
2
x
a
a
r
a
θ
sin
2
1
2
2
2
2
2
x
a
r
x
a
r
11. • For an infinitely long wire:
• From the table of integrals:
2
3
2
2
o
2
3
2
2
o
2
1
2
2
2
2
o
2
o
2
o
x
a
dx
π
4
a
I
μ
x
a
dx
a
π
4
I
μ
B
x
a
a
x
a
dx
π
4
I
μ
B
r
θ
sin
dx
π
4
I
μ
r
θ
sin
dx
π
4
I
μ
dB
2
1
2
2
2
2
3
2
2
x
a
a
x
x
a
dx
12.
a
π
2
I
μ
B
a
π
4
I
μ
2
1
1
a
π
4
I
μ
a
π
4
I
μ
B
a
π
4
I
μ
B
a
a
a
π
4
I
μ
B
x
a
x
a
π
4
a
I
μ
x
a
a
x
π
4
a
I
μ
B
o
o
o
o
2
1
2
2
1
2
o
2
1
2
2
2
1
2
2
o
2
1
2
2
2
o
2
1
2
2
2
o
13. • For a conductor with a finite length:
• From the table of integrals:
x
x
x
x
x
x
x
x
x
x
x
x
2
3
2
2
o
2
3
2
2
o
2
1
2
2
2
2
o
2
o
2
o
x
a
dx
π
4
a
I
μ
x
a
dx
a
π
4
I
μ
B
x
a
a
x
a
dx
π
4
I
μ
B
r
θ
sin
dx
π
4
I
μ
r
θ
sin
dx
π
4
I
μ
dB
2
1
2
2
2
2
3
2
2
x
a
a
x
x
a
dx
14.
2
1
2
2
o
2
1
2
2
o
2
1
2
2
2
1
2
2
o
2
1
2
2
2
1
2
2
o
x
2
1
2
2
2
o
x
2
1
2
2
2
o
x
a
a
π
2
x
I
μ
B
x
a
x
2
a
π
4
I
μ
B
x
a
x
x
a
x
a
π
4
I
μ
B
x
a
x
x
a
x
a
π
4
I
μ
B
x
a
x
a
π
4
a
I
μ
x
a
a
x
π
4
a
I
μ
B
x
x
15. • When the angles are provided:
– express r in terms of a and the angle q:
– Because angles are involved, we need to
change dx to dq:
- Take the derivative of x:
θ
csc
a
θ
sin
a
r
r
a
θ
sin
θ
cot
a
θ
tan
a
x
x
a
θ
tan
dθ
θ
csc
a
dx
dθ
θ
csc
a
dx
2
2
16. • To determine the magnitude of the magnetic field
B, integrate:
1
2
o
θ
θ
o
θ
θ
o
θ
θ 2
2
2
o
θ
θ 2
2
o
2
θ
θ
o
θ
θ
θ
cos
θ
cos
-
a
π
4
I
μ
θ
cos
-
a
π
4
I
μ
B
dθ
θ
sin
a
π
4
I
μ
B
θ
csc
a
dθ
θ
sin
θ
csc
a
π
4
I
μ
B
θ
csc
a
θ
sin
dθ
θ
csc
a
π
4
I
μ
B
r
θ
sin
dx
π
4
I
μ
dB
2
1
2
1
2
1
2
1
2
1
2
1
17. • The magnetic field lines are
concentric circles that
surround the wire in a plane
perpendicular to the wire.
• The magnitude of B is constant
on any circle of radius a.
• The magnitude of the
magnetic field B is
proportional to the current
and decreases as the distance
from the wire increases.
18. Magnetic Field of a Current Loop
• To determine the magnetic field B at the
point O for the current loop shown:
19. • The magnetic field at point O due to the
straight segments AA' and CC' is zero
because ds is parallel to rhat along path AA'
and ds is antiparallel to rhat along path CC'.
• For the curved portion of the conductor
from A to C, divide this into small elements
of length ds.
• Each element of length ds is the same
distance R away from point O.
0
180
sin
0;
0
sin
θ
sin
r̂
ds
r̂
x
ds
20. • Each element of length ds contributes
equally to the total magnetic field B at
point O.
• The direction of the magnetic field B at
point O is down into the page.
• At every point from A to C, ds is
perpendicular to rhat, therefore:
• Integrate from A to C:
ds
90
sin
1
ds
θ
sin
r̂
ds
r̂
x
ds
C
A 2
o
2
C
A
o
C
A R
ds
π
4
I
μ
r
r̂
x
ds
π
4
I
μ
dB
21. • Pull the constant R out in front of the
integral and integrate from A to C:
• The distance s is the arc length from A to C;
arc length s = R·q. Revising the equation:
2
o
C
A
2
o
R
π
4
s
I
μ
ds
R
π
4
I
μ
B
R
π
4
θ
I
μ
R
π
4
θ
R
I
μ
R
π
4
s
I
μ
B o
2
o
2
o
22. Magnetic Field on the Axis of a Circular
Current Loop
• Consider a circular loop of wire of radius R in the
yz plane and carrying a steady current I:
23. • To determine the magnetic field B at a
point P on the axis a distance x from the
center of the loop:
– Divide the current loop into small elements
of length ds.
– Each element of length ds is the same
distance r to point P on the x axis.
– Each element of length ds contributes
equally to the total magnetic field B at point
P.
2
o
r
r̂
x
ds
π
4
I
μ
dB
24. • Express r in terms of R and x:
• Each element of length ds is perpendicular
to the unit vector rhat from ds to point P.
• Substituting into the integral equation:
2
2
2
x
R
r
ds
90
sin
1
ds
θ
sin
r̂
ds
r̂
x
ds
2
2
o
x
R
ds
π
4
I
μ
dB
25. •Notice that the direction of the magnetic
field contribution dB from element of length
ds is at an angle q with the x axis.
26. • At point P, the magnetic field contribution
from each element of length ds can be
resolved into an x component (dBx) and a y
component (dBy).
• The dBy component for the magnetic field
from an element of length ds on one side
of the ring is equal in magnitude but
opposite in direction to the dBy
component for the magnetic field
produced by the element of length ds on
the opposite side of the ring (180º away).
These dBy components cancel each other.
27. • The net magnetic field B at point P is the
sum of the dBx components for the
elements of length ds.
• The direction of the net magnetic field is
along the x axis and directed away from
the circular loop.
θ
cos
x
R
ds
π
4
I
μ
dB
θ
cos
x
R
ds
π
4
I
μ
dB
θ
cos
dB
dB
2
2
o
2
2
o
x
28. • Express R2 + x2 in terms of an angle q:
• Substituting into the integral equation:
2
1
2
2
x
R
R
r
R
θ
cos
2
1
2
2
2
2
o
2
2
o
x
R
R
x
R
ds
π
4
I
μ
dB
θ
cos
x
R
ds
π
4
I
μ
dB
29. • Pull the constants out in front of the
integral:
• The sum of the elements of length ds
around the closed current loop is the
circumference of the current loop; s = 2··R
ds
x
R
π
4
R
I
μ
B
x
R
R
ds
π
4
I
μ
dB
2
3
2
2
o
2
3
2
2
o
30. • The net magnetic field B at point P is given
by:
2
3
2
2
2
o
2
3
2
2
2
o
2
3
2
2
o
x
R
2
R
I
μ
B
x
R
π
4
R
I
μ
π
2
B
R
π
2
x
R
π
4
R
I
μ
B
31. • To determine the magnetic field strength B
at the center of the current loop, set x = 0:
R
2
I
μ
B
R
2
R
I
μ
R
2
R
I
μ
R
2
R
I
μ
B
R
2
R
I
μ
x
R
2
R
I
μ
B
o
3
2
o
6
2
o
3
2
2
o
2
3
2
2
o
2
3
2
2
2
o
32. • For large distances along the x axis from
the current loop, where x is very large in
comparison to R:
3
2
o
6
2
o
3
2
2
o
2
3
2
2
o
2
3
2
2
2
o
x
2
R
I
μ
B
x
2
R
I
μ
x
2
R
I
μ
B
x
2
R
I
μ
x
R
2
R
I
μ
B
33. • The magnetic dipole m of the loop is the
product of the current I and the area A of
the loop: m = I··R2
2
3
2
2
o
2
3
2
2
2
o
2
x
R
π
2
μ
μ
B
x
R
2
R
I
μ
B
π
μ
R
I