A thin spherical shell with radius R1 = 1.00 cm is concentric with a larger thin

Question

A thin spherical shell with radius R1 = 1.00 cm is concentric with a larger thin spherical shell with radius 3.00 cm . Both shells are made of insulating material. The smaller shell has charge q1=+6.00nC distributed uniformly over its surface, and the larger shell has charge q2=9.00nC distributed uniformly over its surface. Take the electric potential to be zero at an infinite distance from both shells.

A) What is the electric potential due to the two shells at the following distance from their common center: r=0?

B) What is the electric potential due to the two shells at the following distance from their common center: r=2 cm?

C) What is the electric potential due to the two shells at the following distance from their common center: r=4cm?

Explanation / Answer

Both the shells are conducting spherical shells.

Charge resides only on the outer surface of conductor.

Charge resides only on the outer surface of each shell.

There is no charge on the inner surface of inner shell

A)

the electric potential due to the two shells at r=0

V = 0 because there is no charge inside of a spherical shell.

B)

the electric potential due to the two shells at r=2

V = kq/r

here r is distance from surface.

the electric potential due to the outer shell is zero.

the electric potential due to the = kq/r = 8.99*10^9*6*10^(-9)/(0.02) = 2697 volt

C)

the electric potential due to the two shells at r=4 cm

V = kq1/r + kq2/r

V = 8.99*10^9*[6*10^(-9)/(0.04) - 9*10^(-9)/(0.04)] = - 674.25 volt

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