Potential

Potential DifferenceThe potential difference between the points A and B is defined as the work done to move a unit charge from point A to point B

Total Work done (W) to move the charge from A to B:

Work done to move unit charge from A to B is potential difference between A and B

…..3

Work done( ) to move the charge for small distance :

….. 1

We know that ….. 2

Eqn.2 in Eqn.1Fig.1

- On which the force is acting

- Potential at a point A - Potential at a point B

Eqn4 ,Eqn.5 in Eqn.3

From Fig.1

….5

…..4We know that

- distance between the charge Q and point A ;

- distance between the charge Q and point B

To find potential (V) at point ‘B’ substitute in Eqn. 1

Potential or Absolute Potential

Potential at any point is defined as the work done to move a unit positive charge from infinite to a that point in an electric field (E)

Potential difference between a point A and B: …...1

- a charge which create the electric field ‘ E ‘

- distance between the charge Q and point A ;

- distance between the charge Q and point B

Relation between Electric field and potential (E and V)

We know that

…………. 1

…………. 2

Compare 1 and 2

Total change (dv )in V(x,y,z) is the sum of partial changes ( ) with respect to x,y,z.

Electric Dipole

The two equal and opposite charges ,which are separated by a small distance, is called electric -dipole or dipole.

Dipole Moment(M)

It is defined as the product of charge(Q) and distance (d)between the charges

Potential and Electric field intensity due to an electric dipole

The potential at point ‘P’ is the sum of potential due to individual charges at that point

- distance between charge and point ‘P’

- distance between charge and point ‘P’

Consider a positive and negative point charges separated by a distance ‘d’.Position of the charges and are (0,0,d/2) and (0,0,-d/2) respectively.

If the point is far away from the charges the difference between and is negligible.

This approximation may not be made in the numerator

In spherical co-ordinate system

We know that

……1

……4

Eqn.2 ,Eqn.3 in Eqn.1

……2

……3

……5

……6

……7

……8

……9

Eqn.7,Eqn.8,Eqn.9 in Eqn.6