Question

A thin infinitely long thread carrying a charge λ per unit length is oriented parallel to the infinite conducting plane. The distance between the thread and the plane is equal to l. Find: 

(a) the modulus of the vector of the force acting on a unit length of the thread; 

(b) the distribution of surface charge density σ (x) over the plane, where x is the distance from the plane perpendicular to the conducting surface and passing through the thread.

Answer 1

(a) The force F₁ on unit length of the thread is given by

F₁ = λ E₁ 

where E₁ is the field at the thread due to image charge :

minus singn means that the force is one of attraction. 

(b) There is an image thread with charge density- λ behind the conducting plane. We calculate the electric field on the conductor. It is