Question

Obtain an expression for electric potential (V) at a point near a point charge ‘Q’.

Answer 1

F = `1/(4 pi epsilon_0) * (Q xx 1)/x^2`

= `(1/(4 pi epsilon_0)) Q/x^2`

dW = −Fdx

= `-(1/(4 pi epsilon_0)) Q/x^2 dx`

Since the test charge is +1, V = W. Therefore,

V = `int_infty^r dW`

= `int_infty^r - (1/(4 pi epsilon_0)) Q/x^2 dx`

= `-Q/(4 pi epsilon_0) int_infty^r x^-2 dx`

= `-Q/(4 pi epsilon_0) [-1/x]_infty^r`

= `Q/(4 pi epsilon_0) (1/r - 0)`

= `(1/(4 pi epsilon_0)) Q/r`

This is the desired expression.