1.

(a) Showthat the normal component of electrostatic field has a discontinuityfrom one side of a charged surface to another given byWhereisa unit vector normal to the surface at a point and σ is thesurface charge density at that point. (The direction of isfrom side 1 to side 2.) Hence show that just outside a conductor, theelectric field is σ (b) Showthat the tangential component of electrostatic field is continuousfrom one side of a charged surface to another. [Hint: For (a), useGauss’s law. For, (b) use the fact that work done byelectrostatic field on a closed loop is zero.]

Answer»


(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.]


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