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Question 16

(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 the surface at a point and σ is the surface charge density at that point. (The direction of is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is σ

 

(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

Electric field on one side of a charged body is E1 and electric field on the other side of the same body is E2. If infinite plane charged body has a uniform thickness, then electric field due to one surface of the charged body is given by,

Where,

= Unit vector normal to the surface at a point

σ = Surface charge density at that point

Electric field due to the other surface of the charged body,

Electric field at any point due to the two surfaces,

Since inside a closed conductor,   = 0,

Therefore, the electric field just outside the conductor is 

 

(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

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