a. (one mark each) i. If a conductor is placed in an external electric field, ex

Question

a. (one mark each) i. If a conductor is placed in an external electric field, explain why there is no electric field inside the conductor.

ii. If a conductor in an external electric field has a cavity, explain what sort of electric field you would expect inside the cavity.

b. (three marks) Consider a spherical cloud of radius R and charge distribution (~r ) = kr2 where k is a constant. Find the electric field inside the sphere. Now, suppose a sphere of radius L, made of conducting material is placed at the centre of the cloud. What is the induced field inside the conducting sphere required to cancel the field from ?

Explanation / Answer

a)

i)

In electrostatics, any surface you draw inside a conductor will have no net electric flux by Gauss' Law, which is an expression of continuity of the field lines:
ii)

The net electric field in the interior of the conducting material must be zero. (The electric field in the cavity,

however, need not be zero.) Knowing this, you can use Gauss's law to find the net charge on the interior

surface of the cavity. Use the following Gaussian surface: an imaginary sphere, centered at the cavity, that

has an infinitesimally larger radius than that of the cavity, so that it encompasses the inner surface of the

cavity

b)

integral(E da) = Qenc / By symmetry of charge distribution E = Er(r) rˆ; also da = da rˆ

integral(E da) = Er(r) 4r 2

Since depends on r, Qenc =integral( d )

Er(r)=1/4*pi*epsilon*r2(integral 0 to r)kr24*pi*r2*dr

=kr3/5epsilon *r(bar)

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