Question

Three concentric spherical metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities s, – s and s respectively. If the shells A and C are at same potential, then the correct relation between a, b and c is –

• A. a + c = b
• B. b + c = a
• C. a – b = c
• D. a + b = c

Answer 1

Answer: (D)

a + b = c

Answer 2

Potential of shell A is,

V_A = $\left( \frac { 4 \pi \mathrm { a } ^ { 2 } \sigma } { \mathrm { a } } \frac { - 4 \pi \mathrm {~b} ^ { 2 } \sigma } { \mathrm {~b} } \frac { + 4 \pi \mathrm { c } ^ { 2 } \sigma } { \mathrm { c } } \right)$

= $\frac { \sigma } { \epsilon _ { 0 } }$ (a – b + c)

Potential of shell C is,

V_C = $\left( \frac { 4 \pi \mathrm { a } ^ { 2 } \sigma } { \mathrm { c } } \frac { - 4 \pi \mathrm {~b} ^ { 2 } \sigma } { \mathrm { c } } \frac { + 4 \pi \mathrm { c } ^ { 2 } \sigma } { \mathrm { c } } \right)$

= $\frac { \sigma } { \epsilon _ { 0 } }$

As V_A = V_C

\ $\frac { \sigma } { \epsilon _ { 0 } }$ (a – b + c) = $\frac { \sigma } { \epsilon _ { 0 } }$

or a – b = or a + b = c