Two concentric conducting spherical shells having radii a and b are charged to q₁ & q₂ respectively. The potential difference between 1 & 2 will be

$\frac{q_1}{4 \pi \varepsilon_0}\left(\frac{1}{a}-\frac{1}{b}\right)$

The potential on the surface of the sphere 1 is given by

$V_1=\frac{1}{4 \pi \varepsilon_0} \frac{q_1}{a}+\frac{1}{4 \pi \varepsilon_0} \frac{q_2}{b}$        . . . (a)

The potential on the surface of the sphere 2 is given by,

$V_2=\frac{1}{4 \pi \varepsilon_0} \frac{q_1}{b}+\frac{1}{4 \pi \varepsilon_0} \frac{q_2}{b}$

$V = V_1-V_2$

$\Rightarrow V=\frac{1}{4 \pi \varepsilon_0} \frac{q_1}{a}-\frac{1}{4 \pi \varepsilon_0} \frac{q_1}{b}$

$\Rightarrow V=\frac{q_1}{4 \pi \varepsilon_0}\left(\frac{1}{a}-\frac{1}{b}\right)$

∴ (C)