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Electrostatic Potential and Capacitance — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectrostatic Potential and Capacitance3 Marks
Question
A small conducting sphere (radius r ) is placed concentrically inside a larger conducting hollow sphere of radius $R$. The big and small spheres are charged with $Q$ and $q(Q>q)$ respectively and kept separate from each other. Calculate the potential difference between the spheres.
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Answer

Potential on the surface of A due to Q $ V=\frac{1}{4 \pi \epsilon_0} \times \frac{Q}{R} $
Potential on the surface of A due to $q$
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$ V=\frac{1}{4 \pi \epsilon_0} \times \frac{q}{R} $
Potential on the surface of $B$ due to $Q=\frac{1}{4 \pi \epsilon_0} \times \frac{Q}{R}$
Potential on the surface of B due to $q=\frac{1}{4 \pi \epsilon_0} \times \frac{q}{r}$
$\therefore$ Potential at $A , B _{s l}=\frac{1}{4 \pi \epsilon_0}\left(\frac{ Q }{ R }+\frac{q}{ R }\right)$
Potential at $B , V _{ B }=\frac{1}{4 \pi \epsilon_0}\left(\frac{ Q }{ R }+\frac{q}{r}\right)$
$\therefore \quad V _{ B }- V _{ A }=\frac{1}{4 \pi \epsilon_0}\left(\frac{q}{r}-\frac{q}{ R }\right)$

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