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Question
Derive an expression for the electric potential at any point along the axial line of an electric dipole.
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 Vq = `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))`
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