Three concentric spherical metallic shells \(A, B\) and \(C\) of radii \(a, b\) and \(c(a < b < c)\) have…

Three concentric spherical metallic shells \(A, B\) and \(C\) of radii \(a, b\) and \(c(a < b < c)\) have charge densities \(\sigma,-\sigma\) and \(\sigma\) respectively. The potential of \(A, B\) and \(C\) are
  1. \(V_{A}=\frac{1}{\varepsilon_{0}}(a+b+c) \sigma\)
  2. \(V_{B}=\frac{1}{\varepsilon_{0}}\left(\frac{a^{2}}{b}-b+c\right) \sigma\)
  3. \(V_{C}=\frac{1}{\varepsilon_{0}}\left(\frac{a^{2}}{c}+\frac{b^{2}}{c}+c\right) \sigma\)
  4. \(V_{A}=V_{B}=V_{C}=\frac{1}{\varepsilon_{0}}(a+b+c) \sigma\)

Solution



\(\frac{Q_{A}}{4 \pi a^{2}}=\sigma\)
\(-\frac{Q_{B}}{4 \pi b^{2}}=-\sigma\)
\(-\frac{Q_{C}}{4 \pi c^{2}}=\sigma\)
\(V_{B}=\frac{Q_{A}}{4 \pi \varepsilon_{0} b}-\frac{Q_{B}}{4 \pi \varepsilon_{0} b}+\frac{Q_{C}}{4 \pi \varepsilon_{0} c}=\frac{1}{\varepsilon_{0}}\left(\frac{a^{2}}{b}-b+c\right)\) ,

Asked in: JEE Mains - Electrostatics - Chapter Test

Practice more Electrostatics questions on Aicharya