Question

A spherical metal (conductor) has a spherical cavity in side. There is a single point charge Q at the cavity center. The total charge on the meta is 0 (a) Describe how the charge is distributed on the E=? sphere. Would the surface charge density be u form at each surface? (b) Draw the electric field lines. c) Find the electric field for a point outside the metal. Express it in terms of r, the distance of the point in question to the center of the metal sphere. Note: Even though the setup has no spherical symmetry, the E-field outside the sphere appears to be spherically symmetric. Try to understand why this should be so A metal sphere with radius a is surrounded by a metallic spherical shell with inner radius b and outer radius c (a < b< c. The two spheres are concentric. The inner metal sphere has +5Q charge and the shell has-3Q charge. We look at a steady state situation where the charges are redistributed on the 30 metals and everything is at rest. (a) Describe how the charge is distributed. (What is the total charge and the surface charge density on each surface?) (b) Find the electric field in each of the four possible regions, i.e., if r denotes the radial coordinate of the point (at which you want to compute the É-field), consider the cases r < a, a<r< b, b<r < c and c< r separately and the determine the electric expression for each region (c) Plot E vs r graph. (Here, as always, E denotes the radialcomponent of the electric field vector, E = Er) For the situation in problem 2 (a) Find the potential on each of the four regions, (i.e, find V as a function of r for all regions (b) Plot V vs r graph. c) Check that i. V is continuous, on all four regions, and 1 iii. V is constant on the conductors.

Answer 1

a)

the charge on outer surface will be same as the charge at the center of cavity

The surface charge density will not be same

surface charge density is given as

charge density = charge/area

since the charge is same , and the area of metal sphere is larger , the surface charge density for the metal sphere will be smaller.

b)

c)

electric field is given as

E = k Q/r²