potential
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Potential
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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
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- 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
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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
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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.
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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
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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.
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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
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……9
Eqn.7,Eqn.8,Eqn.9 in Eqn.6