Question

A nonuniform linear charge distribution given by λ(x) = bx, where b is a constant, is distributed along the x axis from x = 0 to x = +L. If b = 40 nC/m and L = 0.72 m, what is the electric potential (relative to a potential of zero at infinity) at the point y = 2L on the y axis?

Answer 1

The electric potential is given by the equation,

Let us consider a small part of length dx at a distance of x from the x = 0 point on the wire. The charge on this small portion can be written as,

The distance of this part from the point Y = 2L can be written as,

Hence the small potential can be written as,

Substituting values we will get,

We can calculate the total potential by integrating this with the limits x = 0 to x = L = 0.72.

Integrating this we will get,