A charged insulating sphere [radius a = 7cm] is at the center of a conducting sp

Question

A charged insulating sphere [radius a = 7cm] is at the center of a conducting spherical shell (inner radius b = 30cm; outer radius c = 40cm]. The electric field at a point 12cm from the center is measured to be 3 times 10 N/C and points radially outward and the electric field at a point 60cm for the center is of magnitude 100N/C and points radially outward. From this information, find the following: the charge on the insulating sphere the charge on the inner surface of the hollow conducting spherical shell the charge on the outer surface of the hollow conducting spherical shell the net charge on the hollow conducting spherical shell

Explanation / Answer

a)

here by using the formula

E = k * Qinsulator / r1^2

Qinsulator = ( 3 * 10^3 * 0.12^2 ) / ( 9 * 10^9)

Qinsulator = 4.8 * 10^-9 C

d)

again by using gauss law

E2 = k * Qtotal / r2^2

Qtotal = (100 * 0.6^2 ) / ( 9 * 10^9) = 4 * 10^-9 C

Qconductor = Qtotal - Qinsulator = 4 * 10^-9 C - 4.8 * 10^-9 = - 0.8 * 10^-9 C

b)

Qinner = Qinsulator = 4.8 * 10^-9 C

d)

Qouter = Qconductor - Qinner = -0.8 * 10^-9 - 4.8 * 10^-9 = 5.6 * 10^-9 C

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