# Solution - How Much Electrostatic Energy of the First Capacitor is Lost in the Form of Heat and Electromagnetic Radiation? - Electrostatics of Conductors

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#### Question

A 4 µF capacitor is charged by a 200 V supply. It is then disconnected from the supply, and is connected to another uncharged 2 µF capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

#### Solution

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

(vecE_2-vecE_1).hatn=sigma/in_0

Where hatn is a unit vector normal to the surface at a point and σ is the surface charge density at that point. (The direction of hatn is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is σ hatn/in_0

(b) Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.

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A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q.

(a) A charge is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

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