A thin spherical shell with radius R 1 = 4.00cm is concentric with a larger thin

Question

A thin spherical shell with radius R1 = 4.00cm is concentric with a larger thin spherical shell with radius 7.00cm . 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.

Part A

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

Part B

What is the electric potential due to the two shells at the following distance from their common center: r = 5.00cm?

Part C

What is the electric potential due to the two shells at the following distance from their common center: r = 8.00cm?

Part D

What is the magnitude of the potential difference between the surfaces of the two shells?

Part E

Which shell is at higher potential: the inner shell or the outer shell?

Explanation / Answer

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

Electric potential due to sphere = kQ/r

therefore

V (r=0) = Potential due to smaller shell + potential due to larger shell

V (r=0) = k(6*10^(-9)) / (4*10^(-2)) - k(9*10^(-9) / (8*10^(-2)))= 1350 - 1350=0 V

What is the electric potential due to the two shells at the following distance from their common center: r = 5.00cm ?

V (r=5cm) = Potential due to smaller shell + potential due to larger shell

V (r=5cm) = k(6*10^(-9)) / (5*10^(-2)) - k(9*10^(-9) / (8*10^(-2))) = 1080-1350 = - 270 V

What is the electric potential due to the two shells at the following distance from their common center: r = 9.00cm ?

V (r=9cm) = Potential due to smaller shell + potential due to larger shell

V (r=9cm) = k(6*10^(-9)) / (9*10^(-2)) - k(9*10^(-9) / (9*10^(-2))) = 600-900 = -300 V

What is the magnitude of the potential difference between the surfaces of the two shells?

potential diffrence between two shell =  Potential due to smaller shell - potential due to larger shell

potential diffrence between two shell = k(6*10^(-9)) / (9*10^(-2)) - k(-9*10^(-9) / (9*10^(-2))) = 600+900 = 1500 V

Which shell is at higher potential: the inner shell or the outer shell?

inner shell is at higher potential and outer is at lower potential.

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