Question

A small conducting sphere of radius r is lying concentrically inside a bigger hollow conducting sphere of radius R. The bigger and smaller sphere are charged with Q and q(Q > q) and are insulated from each other. The potential difference between the sphere will be –

• A. $\frac { 1 } { 4 \pi \varepsilon _ { 0 } }$ $\left( \frac{q}{r}–\frac{q}{R} \right)$
• B. $\frac { 1 } { 4 \pi \varepsilon _ { 0 } }$ $\left( \frac{q}{R}–\frac{Q}{r} \right)$
• C. $\frac { 1 } { 4 \pi \varepsilon _ { 0 } }$ $\left( \frac{q}{r}–\frac{Q}{R} \right)$
• D. $\frac { 1 } { 4 \pi \varepsilon _ { 0 } }$ $\left( \frac{Q}{R} + \frac{q}{r} \right)$

Answer 1

Answer: (A)

\frac { 1 } { 4 \pi \varepsilon _ { 0 } }$$\left( \frac{q}{r}–\frac{q}{R} \right)

Answer 2

V_A = $\frac { \mathrm { kq } } { \mathrm { r } }$ +

V_B = $\frac { \mathrm { kq } } { \mathrm { R } }$ +

\ V_A – V_B = $\frac { \mathrm { kq } } { \mathrm { r } }$ – $\frac { \mathrm { kq } } { \mathrm { R } }$