Question

There are two concentric hollow conducting spherical shells of radii \( r \) and \( R(R>r) \). The charge on the outer shell is \( Q \). What charge should be given to the inner shell, so that the potential at a point \( P \), at a distance \( 2 R \) from the common centre, is zero? 

(1) \( \frac{-Q r}{R} \)

(2) \( \frac{-Q R}{r} \)

(3) \( \frac{-2 Q R}{r} \)

(4) \( -Q \)

Answer 1

The correct option is (4) -Q

We are given that, for the circle of radius R, the charge is Q. Potential can be defined as the work done to bring a charge from a reference point to a particular point. We can find the value of charge in the inner circle by using the formula,

\(V = \frac{Q}{4 \pi\varepsilon_0 R} + \frac{q}{4 \pi\varepsilon_0 R}\)

When we equate it to zero, we get

\(V = \frac{Q}{4 \pi\varepsilon_0 R} + \frac{q}{4 \pi\varepsilon_0 R} = 0\)

\(\frac{1}{4\pi\varepsilon_0R} \times (Q + q) = 0\)

We take the constant to the other side and get

Q + q = 0

q = -Q

This gives us the value of charge on the inner circle to be negative of the charge on the outer circle.