Consider an infinitely long wire with charge per unit length centered at (x, y) = (0, d) parallel to the z-axis. A) Find the potential due to this line charge referenced to the origin so that ϕ=0.

Given that,

Charge per unit length = λ

Point (x, y)=(0. d) parallel to the z axis

We know that,

The electric field due to the infinitely long wire is

The electric potential is

....(I)

Here,

We need to calculate the potential due to this line charge

Using equation (I)

On integratinting

Put the value of r

Hence, The potential due to this line charge is

grav potential energy