A spherical conductor has two spherical cavities A charge q1

A spherical conductor has two spherical cavities. A charge q_1 = -8.00 mu C is placed at the center of one cavity and a charge q_2 = +5.00 mu C is placed at the center of the other cavity. Additionally, a charge q = 6.00 mu C is placed on the conductor. What is the charge on the surface of the smaller cavity? What is the charge on the surface of the bigger cavity? What is the charge on the outer surface of the conductor? What is the magnitude of the electric field in the smaller cavity? What is the magnitude of the electric field in the larger cavity? What is the magnitude of the electric field outside the conductor? Sketch the electric field lines in the two cavities and in the region outside the Conductor. What is the electrostatic force on q_1?

Solution

a)

Answer is 8 uC

The Field inside the spherical cavity is independent of anything outside ,so a charge -q₁ i.e 8 uC is uniformly distribuited to cancel the field from Q=6 uC

b)

Answer is -5 uC

The Field inside the spherical cavity is independent of anything outside ,so a charge -q₂ i.e -5 uC is uniformly distribuited to cancel the field from Q=6 uC

C)

Charge on the outer surface

Q_outer =8-5 =3 uC

d)

Answer is E=0

Electric field inside a conductor is zero

e)

E=0