Question

1. Consider two concentric spherical conducting shells of radii a and b (b > a) kept at potentials V1 and V2, respectively. For the following parts, express all your answers in terms of V1, V2, a, and b.

(a) Calculate the charges q1 and q2 on the two shells.

(b) Calculate the potential in the region between the shells.

(c) Calculate the work that needs to done to set up this charge configuration.

(d) The shells are now connected to each other by a conducting wire. What are the new charges q ′ 1 and q ′ 2 on the two shells?

Answer 1

Electric pot. at any point inside the sphere with radius r<R and charge q is kq/R

at any point outside the sphere r>R is kq/r

q1 and q2 are charge on A and B

k q1/a + kq2/b = V1 and

k q1/b + kq2/b = V2 - solving he two eq. we get

q1 = ab(V₁ - V₂) /k(b-a) ; q₂ = (b²V₂ - abV₁ )/k(b-a)

b) Pot. any where between the shells a<r<b

= V₁ a/r + V₂

c) work done = (V₂ - V₁) , is the pot. energy of the system of charges.

d)When they are connected by wire both are at same potential (V1 +V2)/2

= q_a / ka = q_b /kb

charge on shell 1 q_a = ka(V1 +V2)/2

q_b = kb(V1 +V2)/2