There are three co-centric conducting spherical shells A, B and C of radii , and respectively and they are charged with charges , and respectively. The potentials of the spheres A, B and C respectively, are: [2026]

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Solution

Q.
There are three co-centric conducting spherical shells A, B and C of radii $a$ , $b$ and $c$ respectively $(c > b > a)$ and they are charged with charges $q_{1}$ , $q_{2}$ and $q_{3}$ respectively. The potentials of the spheres A, B and C respectively, are: [2026]

1 $\frac{1}{4 π ε_{0}} (\frac{q_{1} + q_{2} + q_{3}}{a}), \frac{1}{4 π ε_{0}} (\frac{q_{1} + q_{2} + q_{3}}{b}), \frac{1}{4 π ε_{0}} (\frac{q_{1} + q_{2} + q_{3}}{c})$

2 $\frac{1}{4 π ε_{0}} (\frac{q_{1}}{a} + \frac{q_{2}}{b} + \frac{q_{3}}{c}), \frac{1}{4 π ε_{0}} (\frac{q_{1} + q_{2}}{b} + \frac{q_{3}}{c}), \frac{1}{4 π ε_{0}} (\frac{q_{1} + q_{2} + q_{3}}{c})$

3 $\frac{1}{4 π ε_{0}} (\frac{q_{1}}{a} + \frac{q_{2}}{b} + \frac{q_{3}}{c}), \frac{1}{4 π ε_{0}} (\frac{q_{1} + q_{2} + q_{3}}{b}), \frac{1}{4 π ε_{0}} (\frac{q_{1} + q_{2} + q_{3}}{c})$

4 $\frac{1}{4 π ε_{0}} (\frac{q_{1} + q_{2} + q_{3}}{a}), \frac{1}{4 π ε_{0}} (\frac{q_{1} + q_{2}}{b} + \frac{q_{3}}{c}), \frac{1}{4 π ε_{0}} (\frac{q_{1}}{a} + \frac{q_{2}}{b} + \frac{q_{3}}{c})$

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