For the configuration shown in the figure below, suppose a = 5.00 cm, b = 20.0 c
ID: 1418749 • Letter: F
Question
For the configuration shown in the figure below, suppose a = 5.00 cm, b = 20.0 cm, and c = 25.0 cm. Furthermore, suppose the electric field at a point 18.0 cm from the center is measured to be 3.30 103 N/C radially inward and the electric field at a point 50.0 cm from the center is of magnitude 183 N/C and points radially outward. From this information, find the following. (Include the sign of the charge in your answer.)
(a) the charge on the insulating sphere
(b) the net charge on the hollow conducting sphere
(c) the charge on the inner surface of the hollow conducting sphere
(d) the charge on the outer surface of the hollow conducting sphere
Explanation / Answer
Solving the question will require knowledge of following
1)Gauss Theorem
Net Electric Flux=Charge enclosed/ where is permittivity of vaccum
2)Electric field inside{between outer and inner surface} a conductor is always zero
3)Electric field at distance
1)Net charge{q1} on insulating sphere will be uniformly distributed
using guass theorem electric field at distance 18cm =k(q1)/(18*10^-2)^2
q1 = 118.8 * 10^-10 C
2)at distance 50cm=k(q1+q2)/(50*10^-2)^2.... where q2 is net charge on conducting surface
q1+q2 = 50.833 * 10^-10
q2 = -67.967 * 10^-10C
3)since electric field inside{between outer and inner surface} conductor is zero
any sphere imagined inside the conductor sphere will have zero charge enclosed [guass theorem]
charge on inner surface of the hollow conducting sphere =-q1
4)charge on the outer surface of the hollow conducting sphere=q2+q1
q1+q2 = 50.833 * 10^-10