Question

(a) Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by

Where is a unit vector normal to themsurface at a point and σ is the surface charge density at that point. (The direction of n cap is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is σ n cap/ε_o

(b) Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another. [Hint: For (a), use Gauss’s law. For, (b) use the fact that work done by electrostatic field on a closed loop is zero.]

Answer 1

(a) Electric field on one side of a charged body is E₁ and electric field on the other side of the same body is E_2. If infinite plane charged body has a uniform thickness, then electric field due to one surface of the charged body is given by,

(b) When a charged particle is moved from one point to the other on a closed loop, the work done by the electrostatic field is zero. Hence, the tangential component of electrostatic field is continuous from one side of a charged surface to the other.