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Capacitance of a Random Conductor

A spherical m...

Question

A spherical metal shell A of radius RA and a solid metal sphere B of radius RB(< RA) are kept far apart and each is given charge ‘+Q’. Now they are connected by a thin metal wire. Then

E_{A}^{on surface} < E_{B}^{o n s u r f a c e}

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E_{A}^{inside} = 0

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\frac{σ_{A}}{σ_{B}} = \frac{R_{B}}{R_{A}}

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Q_{A} > Q_{B}

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Solution

The correct option is D $Q_{A} > Q_{B}$
After connection,
$V_{A} = V_{B}$
$\Rightarrow \frac{q_{A}}{R_{A}} = \frac{q_{B}}{R_{B}}$
$E_{A (inside)} = 0$
$\Rightarrow q_{A} > q_{B}$
$\frac{σ_{A}}{σ_{B}} = \frac{q_{A}}{q_{B}} \times \frac{R_{B}^{2}}{R_{A}^{2}} = \frac{R_{B}}{R_{A}}$
$\frac{E_{A}}{E_{B}} = \frac{σ_{A}}{σ_{B}} = \frac{R_{B}}{R_{A}}$

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