A thin spherical shell with radius R1 = 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

given that,

R1 = 4cm and R2= 7cm

q1 = +6.00nC = 6 x 10-9and 9.00 nC = 9 x 10-9

K = 8.99 x 109

Part (A) electric potential due to the two shells at the following distance from their common center: r = 0 ie r<R1,

E = kq1/R1 + kq2/ R2, putting the values, we get E= 25.035

(B)  electric potential due to the two shells at the following distance from their common center: r = 5.00cm, will be given by

E = kq1/r + kq2/R2 Putting the value we get, E = 22.34

Part (C)electric potential due to the two shells at the following distance from their common center: r = 8.00cm,will be given by

E = K (q1 + q2) / r, putting the value we get , E = 16.65

Part (E)

The inner surface is at heigher potential

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