This document provides an overview of key concepts in electricity and electrostatics, including: 1. Electric charge is a fundamental property of matter that can be positive or negative and is measured in coulombs. Charging methods include friction, conduction, and induction. 2. Coulomb's law describes the proportional relationship between the electrostatic force between two point charges and the product of their magnitudes over the square of the distance between them. 3. Electric fields are defined as the force exerted on a test charge at a point. Electric flux is the number of field lines passing through a given area. Gauss's law relates electric flux to the enclosed charge. 4. Electric potential is the work required

1. Certificate Course
on
Techniques of Problem Solving in Physics
Electric charge
• It is a basic property of matter carried by some elementary particles that governs how the
particles are affected by an electric or magnetic field. Electric charge, which can be
positive or negative, occurs in discrete natural units and is neither created nor destroyed.
• Electric charge is a scalar quantity.
• The electric charge is measured using coulomb.
Various properties of charge include the following:
• Additivity of Electric Charge
• Conservation of Electric Charge
• Quantization of Electric Charge
Coulomb’s Law
The magnitude of the electrostatic force of attraction or repulsion between two-point
charges is directly proportional to the product of the magnitudes of charges and inversely
proportional to the square of the distance between them.
F =
1
4π𝜖0
∙
q1 ∙ q2
r2
An uncharged object can be charged in three different ways as follows:
Charging by friction
When two objects are rubbed against each other, charge transfer takes place. One of the
objects loses electrons while the other object gains electrons. The object that loses electrons
becomes positively charged and the object that gains electrons becomes negatively charged. Both
the objects get charged due to friction and this method of charging is commonly known as
electrification by friction.
Charging by conduction
The method of charging an uncharged object by bringing it close to a charged object is
known as charging by conduction. The charged conductor has an unequal number of protons and
electrons, hence when an uncharged conductor is brought near it, it discharges electrons to
stabilise itself.
Charging by Induction
The process of charging an uncharged conductor by bringing it near a charged conductor
without any physical contact is known as charging by induction.
Electric Field
Electric field at a point in the space is measured as the force acting on the unit positive
charge at that point.
E =
1
4πϵ0
∙
q
r2

2. Electric Flux
• The total number of electric field lines passing a given area is defined as the electric flux.
• Line of force is a path followed by an electric charge free to move in an electric field
• Lines of force are lines in any such force field the tangent of which at any point gives the
field direction at that point and the density of which gives the magnitude of the field.
Properties of Electric Field Lines:
• The field lines never intersect each other.
• The field lines are perpendicular to the surface of the charge.
• The magnitude of charge and the number of field lines, both are proportional to each
other.
• The start point of the field lines is at the positive charge and end at the negative charge.
• For the field lines to either start or end at infinity, a single charge must be used.
Gauss Law
It states that the total electric flux out of a closed surface is equal to the charge enclosed divided
by the permittivity.
φ =
q
ε0
φ = ∫E ⋅ n
̂da
𝑆
Electric Potential
• The amount of work needed to move a unit charge from a reference point to a specific
point against an electric field.
V =
W
Q
• Electric potential can be thought of as the potential energy per unit charge. Therefore, the
work done in moving a unit charge from one point to another is equal to the difference in
potential energies at each point.
• Electric potential is expressed in units of joules per coulomb (i.e., volts)
V =
1
4πϵ0
∙
q
r
Equipotential Surface
• A surface which has same electrostatic potential at every point on it, is known as
equipotential surface.
• Equipotential surfaces do not intersect each other as it gives two directions of electric
field at intersecting point which is not possible.
• Equipotential surfaces are closely spaced in the region of strong electric field and vice-
versa.
• Electric field is always normal to equipotential surface at every point of it and directed
from one equipotential surface at higher potential to the equipotential surface at lower
potential.
• Work done in moving a test charge from one point of equipotential surface to other is
zero.

3. Electrostatic Potential Energy The work done against electrostatic force gets stored as potential
energy. This is called electrostatic potential energy
Electric Current
• Current is the rate at which charge flows past a point on a circuit.
• Direct current (DC) is the one directional flow of electric charge.
• Alternating current (AC) is an electric current which periodically reverses direction and changes
its magnitude continuously with time.
• Unit ampere