Question

Charges $Q,2Q$ and $-Q$ are given to three concentric conducting spherical shell $\text{A, B}$ and $\text{C}$ respectively as shown in figure. The ratio of charges on the inner and outer surfaces of shell $\text{C}$ will be

• A. $+\frac{3}{4}$
• B. $-\frac{3}{4}$
• C. $\frac{3}{2}$
• D. $-\frac{3}{2}$

Answer 1

The correct option is D $-\frac{3}{2}$

We know that the total charge inside of each conducting shell is zero.
According to this Gauss law of charge distribution the charges will be distributed among surfaces of shells as shown in figure.


From figure, the charge on inner surface of outer shell $=-3Q$
and the charge on outer surface of outer shell $=-Q+3Q=2Q$

The required ratio $=\frac{-3Q}{2Q}=-\frac{3}{2}$

Hence, option (d) is correct answer.