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Derivation

Sum

Derive an expression for the electric potential at any point along the axial line of an electric dipole.

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#### Solution

Suppose P is a point on the axial position of the dipole.

Length of dipole = 2a

Suppose point P is at the distance 'r' from the center of the dipole.

The potential at a point is V = `1/(4piε_0).Q/r`

So, the potential at P due to q is V_{q }= `1/(4piε_0).q/(a+r)`

Potential at P due to -q is V_{-q} = `1/(4piε_0).(-q)/(a-r)`

The total potential at P is `V = V_q + V_(-q)`

= `1/(4piε_0).q/((a + r)) + 1/(4piε_0).(-q)/((r - a))`

= `q/(4piε_0)[1/((a + r)) + 1/((a - r))]`

V = `q/(4piε_0).(2a)/((a^2 - r^2))`

Concept: Potential Due to an Electric Dipole

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