A first conductor is a hollow sphere of radius R1 centered at the origin; the co

Question

A first conductor is a hollow sphere of radius R1 centered at the origin; the conductor carries a net charge Q1. A second conductor is another hollow sphere of radius R2 > R1, also centered at the origin; this conductor carries a net charge Q2.

(a) What is the potential outside the larger sphere?

(b) What is the potential on the larger sphere?

(c) What is the potential between the spheres?

(d) What is the potential on the smaller sphere?

(e) What is the potential inside the smaller sphere?

(f) How do the preceding answers change if a point charge q is placed at the origin?

Explanation / Answer

a)
at r > R2

V = V1 + V2

= k*Q1/r + k*Q2/r

= k*(Q1+Q2)/r

b) at r = R2

V = V1 + V2

= k*Q1/R2 + k*Q2/R2

= k*(Q1+Q2)/R2

c)at R1 < r < R2

V = V1 + V2

= k*Q1/r + k*Q2/R2

d) at r = R1

V = V1 + V2

= k*Q1/R1 + k*Q2/R2

e) at r < R1

V = V1 + V2

= k*Q1/R1 + k*Q2/R2

f) when we place q at the origin

at r > R2

V = V1 + V2 + V3

= k*Q1/r + k*Q2/r + k*q/r

= k*(Q1+Q2+q)/r

b) at r = R2

V = V1 + V2 + v3

= k*Q1/R2 + k*Q2/R2 + k*q/R2

= k*(Q1+Q2+q)/R2

c)at R1 < r < R2

V = V1 + V2 + V3

= k*Q1/r + k*Q2/R2 + k*q/r

d) at r = R1

V = V1 + V2 + v3

= k*Q1/R1 + k*Q2/R2 + k*q/r

e) at r < R1

V = V1 + V2 + v3

= k*Q1/R1 + k*Q2/R2 + k*q/r

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