Question 494: Electrostatics & Capacitance

Question

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge
densities $$ + \sigma $$, $$ - \sigma $$ and $$ + \sigma $$ respectively. The potential of shell B is :

Accepted Answer

Let charge of shell A, B and C are Q
A
,  Q
B
and  Q
C
respectively.
Potential of B shell will be due to charge Q
A
, Q
B
and Q
C
.
Here charge Q
A
is inside of  the shell B and Q
B
is on the surface of the shell B in both cases you have to take the radius of the shell B, while calculating potential of shell B.
Charge Q
C
is outside of the shell B so take radius of shell C for calculating potential of shell B.
$$	herefore$$ V
B
= V$$_{{Q_a}}$$ + V$$_{{Q_b}}$$ + V$$_{{Q_c}}$$
= $${1 \over {4\pi {\varepsilon _0}}}$$  $$\left[ {{{4\pi {a^2}\left( { + \sigma } ight)} \over b} + {{4\pi {b^2}\left( { - \sigma } ight)} \over b} + {{4\pi {c^2}\left( { + \sigma } ight)} \over c}} ight]$$
= $${1 \over {4\pi {\varepsilon _0}}}$$ $$ 	imes $$ 4$$\pi $$$$\sigma $$ $$\left[ {{{{a^2}} \over b} - {{{b^2}} \over b} + c} ight]$$
= $${\sigma  \over {{\varepsilon _0}}}\left[ {{{{a^2} - {b^2}} \over b} + c} ight]$$

Answer

$${\sigma  \over { \in {}_0}}\left[ {{{{b^2} - {c^2}} \over c} + a} \right]$$

Answer

$${\sigma  \over { \in {}_0}}\left[ {{{{a^2} - {b^2}} \over a} + c} \right]$$

Answer

$${\sigma  \over { \in {}_0}}\left[ {{{{a^2} - {b^2}} \over b} + c} \right]$$

Answer

$${\sigma  \over { \in {}_0}}\left[ {{{{b^2} - {c^2}} \over b} + a} \right]$$

Electrostatics & Capacitance

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $ + \sigma , - \sigma and + \sigma $ respectively. The potential of shell B is :

Choose the correct answer: