Electrostatic potential

Electric Dipole

Capacitors

Grouping of Capacitors

Electric flux is measured in

Mathematically,

This law gives a relation between the electric flux through any closed hypothetical surface (called Gussian surface) and the charge enclosed by any surface. It states, " The electric flux through any closed surface is equal to times the 'net' charge enclosed by the surface."

That is,

Gauss's law is useful when there is symmetry in the charge distribution, as in case of uniformly charged sphere, long cylinders, and flat sheets. In such cases, it is possible to find a simple Gaussian surface over which the surface integral given by

(c) A gaussian sphere with radius r < R.

When outside the shell of charge, as in Figure 8 (a), the left side of Gauss's equation reduces to the following expression:

Thus, the electric field outside a charged sphere is the same as if the same amount of charge were concentrated in a point located at the center of the sphere. The gaussian surface inside the sphere encloses no charge, and therefore, there is

Imagine moving a small test charge q′ from point A to point B in the uniform field between parallel plates.
The work done in transferring the charge equals to the product of the force on the test charge and the
parallel component of displacement.
This work can also be expressed in terms of E from the definition of electric field as the ratio of
force to charge:** W · d, E = F/ q and W = q′ **. See Figure .

where a test charge moves over a line integral from point A to point B along path s in an electric field** (E)**.
** For the special case of Parallel Plates ** :

where** V** is the potential difference between the plates, measured in units of volts (V):

The** electric potential due to a point charge** (q) at a distance (r) from the point charge is

** Figure
**
Work is done when q′ moves from position

A to B in an electric field E.

Work is change in potential energy:** U B − U A = q′ Ed ** .

In general, the electrostatic potential difference, sometimes called the

where a test charge moves over a line integral from point A to point B along path s in an electric field

where

The

A to B in an electric field E.

Equipotential surfaces are surfaces **where no work is required to move a charge from one point to another ** .
The equipotential surfaces are always **perpendicular to the electric field lines ** .

Equipotential lines are two-dimensional representations of the intersection of the surface with the plane of the diagram. In Figure , equipotential lines are shown for (a) a uniform field, (b) a point charge, and (c) two opposite charges.

** Figure**
Equipotential lines for (a) a uniform electric field, (b) a point charge, and (c) two opposite charges.

The**Electrical Potential Energy** of a pair of point charges separated by a distance r is

Equipotential lines are two-dimensional representations of the intersection of the surface with the plane of the diagram. In Figure , equipotential lines are shown for (a) a uniform field, (b) a point charge, and (c) two opposite charges.

The

Two equal and opposite point charges placed at a short distance apart constitute an electric dipole.

## Electric Dipole Moment

Electric dipole moment is a vector directed along the axis of the dipole, from the negative to the positive charge. The magnitude of the dipole moment is

where 2a is the distance between the two charges.

##
Electric Dipole In A Uniform Electric Field

If the electric field strength E at every point in the field is the same, then it is said to be a**uniform electric field ** . Consider an electric dipole consisting of two equal and
opposite point charges +q and –q separated by a distance 2a.

Electric dipole moment is a vector directed along the axis of the dipole, from the negative to the positive charge. The magnitude of the dipole moment is

where 2a is the distance between the two charges.

If the electric field strength E at every point in the field is the same, then it is said to be a

Capacitor is an arrangement of two conductors carrying

The following points may be carefully noted: (i) The net charge on the capacitor as a whole is zero. (ii) The positively charged conductor is at a higher potential than negatively charged conductor. The potential difference V between the conductors is proportional to the magnitude of charge Q and the ratio Q/V is known as capacitance C of the capacitor.

(iii) In a circuit, a capacitor is represented by the symbol:

Consider a parallel plate capacitor consisting of two parallel plates of area A square metres separated by a distance d as shown in the figure.

When the capacitor store charge, capacitors are also storing energy: Energy,

The capacitance of a set of charged parallel plates is increased by the insertion of a dielectric material. The capacitance is

Replacing a combination of capacitors by a single equivalent capacitor is called

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