ElectrostaticsMedium
Question
There are three co-centric conducting spherical shells $A,B$ and C of radii $a,b$ and c respectively. The potential of the spheres $A,B$ and C respectively, are :
Options
A.$\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1} + q_{2} + q_{3}}{a} \right),\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1} + q_{2} + q_{3}}{\text{ }b} \right),\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1} + q_{2} + q_{3}}{c} \right)$
B.$\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1} + q_{2} + q_{3}}{a} \right),\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1} + q_{2}}{\text{ }b} + \frac{q_{3}}{c} \right),\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1}}{a} + \frac{q_{2}}{\text{ }b} + \frac{q_{3}}{c} \right)$
C.$\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1}}{a} + \frac{q_{2}}{\text{ }b} + \frac{q_{3}}{c} \right),\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1} + q_{2}}{\text{ }b} + \frac{q_{3}}{c} \right),\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1} + q_{2} + q_{3}}{c} \right)$
D.$\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1}}{a} + \frac{q_{2}}{\text{ }b} + \frac{q_{3}}{c} \right),\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1} + q_{2} + q_{3}}{\text{ }b} \right),\frac{1}{4\pi\epsilon_{0}}\left( \frac{q_{1} + q_{2} + q_{3}}{c} \right)$
Solution
$${V_{A} = \frac{{Kq}_{1}}{a} + \frac{{Kq}_{2}}{\text{ }b} + \frac{{Kq}_{3}}{c} = \frac{1}{4\pi\varepsilon_{0}}\left( \frac{q_{1}}{a} + \frac{q_{2}}{\text{ }b} + \frac{q_{3}}{c} \right) }{V_{B} = \frac{{Kq}_{1}}{\text{ }b} + \frac{{Kq}_{2}}{\text{ }b} + \frac{{Kq}_{3}}{c} = \frac{1}{4\pi\varepsilon_{0}}\left( \frac{q_{1} + q_{2}}{\text{ }b} + \frac{q_{3}}{c} \right) }{V_{C} = \frac{{Kq}_{1}}{c} + \frac{{Kq}_{2}}{c} + \frac{{Kq}_{3}}{c} = \frac{1}{4\pi\varepsilon_{0}}\left( \frac{q_{1} + q_{2} + q_{3}}{c} \right)}$$
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