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Capacitance of a Random Conductor

A spherical m...

Question

A spherical metal Shell $A$ of radius $R_{A}$ and a solid metal sphere $B$ of radius $R_{e} (< R_{A})$ are kept far apart and each is given charge $^{'} + Q^{'}$ . Now they are connceted by a thin metal wire. Then

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

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E_{A}^{i n s i d e} = 0

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Q_{A} > Q_{B}

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

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Solution

The correct option is D $\frac{σ_{A}}{σ_{B}} = \frac{R_{B}}{R_{A}}$
After connection,

$V_{A} = V_{B}$

$\Rightarrow \frac{q_{A}}{R_{A}} = \frac{q_{B}}{R_{B}}$

$E_{A (i n s i d e)} = 0$

$\Rightarrow q_{A} > q_{B}$

$\frac{σ_{A}}{σ_{B}} = \frac{q_{A}}{q_{B}} \times \frac{R_{B}^{2}}{R_{A}^{2}} = \frac{R_{B}}{R_{A}}$

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

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