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?

Answer 1

part A) at r = 0 ,

The electric potential, V = k*q1/R1 + k*q2/R2

= 9*10^9*6*10^-9/0.04 + 9*10^9*(-9*10^-9)/0.07

= 193 V <<<<<<-------------Answer

part B) at r = 5 cm

The electric potential, V = k*q1/r + k*q2/R2

= 9*10^9*6*10^-9/0.05 + 9*10^9*(-9*10^-9)/0.07

= -77.1 V <<<<<<-------------Answer

part C) at r = 8 cm = 0.08 m

The electric potential, V = k*q1/r + k*q2/r

= 9*10^9*6*10^-9/0.08 + 9*10^9*(-9*10^-9)/0.08

= -338 V <<<<<<-------------Answer

part D)

potential differenec between the two shells,

delta_V = potential on inner sphere - potential on outer sphere

= (k*q1/R1 + k*q2/R2) - (k*q1/R2 + k*q2/R2)

= k*q1*(1/R1 - 1/R2)

= 9*10^9*6*10^-9*(1/0.04 - 1/0.07)

= 578 V <<<<<<<<<----------------Answer

part E) The inner shell.