question_answer 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  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                   (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:

Consider a sheet of charge having, charge density  E on either side of the sheet, perpendicular to the plane of sheet, has same magnitude at all points equidistant from the sheet.                 Consider a pill box of length r on each side of the sheet.                 Electric flux over the edges                                                   According to Gauss' law,                                 i.e.                 For a uniform thick plate, electric field Intensity at both sides is given by                 Net intensity                  The electric field tangential to the plate is continuous throughout.