A very long conducting cylinder (length L) of radius R (R

+1

We have to find electric potential V at a distance r.

a) For r>R,

The electric field in the cylinder is given by

E. A equating it to the other electric field given by

б. A/ε₀

Here the area of cylinder is given by = 2*3.14*r*L

While for the outside, the area = 2*3.14*R*L

Equating both, we get

E = бR/rε₀

Now,

The potential difference is given as:

ΔV = - бR/rε₀ and integrating right side with respect to dr under limits r and R.

Where ΔV = V₀-V

So solving we get

V₀=V-бR/ε₀ln (r/R)

b) For r
There will be no electric field produced as E=0

So ultimately Vin = V

c) V=0 at r = infinity.