Question

A metal sheet is moved with constant acceleration 'a’ parallel to its plane. Does any charge develop on its surfaces, which are perpendicular to its motion?

Answer 1

As the metal plate is accelerated, the electrons inside also possess the same acceleration. A force may be applied on an electron, only when an electric field is created. So there must develop charges on the faces that are perpendicular to the direction of motion, so that there develops an electric field inside the metal plate. The front face will be charged positively, and the rear one negatively. If E is the intensity of electric field, then surface density of charge σ developed is given by 

e E = ma

or e\(\frac{\sigma}{ɛ_o}\)= ma [∵ E = \(\frac{\sigma}{ɛ_o}\)]

or σ = \(\frac{ɛ_oma}{e}\)