Physics question

Question

A long thin wire is uniformly charged with the charge per unit length λ. The electric field at a distance r

from the wire is E=2kλ/r pointing away from the wire.

(a) Find the electric potential V(r) as a function of the distance from the wire.

A long thick conducting wire of radius R is uniformly charged with the charge per unit length λ.

(b) Find the electric potential V(r) as a function of the distance from the axis of the wire

(c) Find the surface charge density σ on the wire.

Answer 1

The relation between Potential V and electric field E is given as

E = - dV/dr

So dV = -Edr

Integrating

V= -∫Edr limits from 0 to r

plug in E ==2kλ/r

V=- ∫(2kλ/r ) dr = - 2kλ ∫dr/r = 2kλlog r

For solid conducting cylinder V = 2kλlog R for all points inside cylinder

and for all points out sid

V= 2kλlog r, wher r= distance from wire to the point ( Shortest distance)