- Introduction
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- Electric potential energy
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- Electric Potential
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- Electric potential due to a point charge
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- Relation between electric fiels and electric potential
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- Equipotential surfaces
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- Potential due to an electric dipole
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- Work done in rotating an electric dipole in an electric field
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- Potential energy of dipole placed in uniform electric field

- We now move towards the electric potential which is potential energy per unit charge.

- Thus electrostatic potential at any point of an electric field is defined as potential energy per unit charge at that point.

- Electric potential is represented by letter V.

V=U/q' or U=q'V (6)

- Electric potential is a scalar quantity since both charge and potential energy are scalar quantities.

- S.I. unit of electric potential is Volt which is equal to Joule per Coulumb. Thus,

1 Volt = 1 JC^{-1}

- In equation 4 if we divide both sides by q' we have

where V(r_{1}) is the potential energy per unit charge at point R and V2) is potential energy per unit charge at point S and are known as potential at points R and S respectively.

- Again consider figure 1. If point S in figure 1 would be at infinity then from equation 7

Since potential energy at infinity is zero therefore V(∞)=0. Therefore

hence electric potential at a point in an electric field is the ratio of work done in bringing test charge from infinity to that point to the magnitude of test charge.

- Dimensions of electric potential are [ML
^{2}T^{-3}A^{-1}] and can be calculated easily using the concepts of dimension analysis.

- Consider a positive test charge +q is placed at point O shown below in the figure.

- We have to find the electric potential at point P at a distance r from point O.

- If we move a positive test charge q' from infinity to point P then change in electric potential energy would be

- Electric potential at point P is

- Potential V at any point due to arbitrary collection of point charges is given by

- here we see that like electric field potential at any point independent of test charge used to define it.

- For continous charge distributions summation in above expressin will be replaced by the integration

where dq is the differential element of charge distribution and r is its distance from the point at which V is to be calculated.

Class 12 Maths Class 12 Physics