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

Engineering

Physics

Electric Potential Energy and Electric Potential

Question

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

Q_A > Q_B

$E_{A}^{on surface} < E_{B}^{on surface}$

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

$E_{A}^{inside} = 0$

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$\frac{{kQ}_{A}}{R_{A}} = \frac{{kQ}_{B}}{R_{B}}$ [Final potential will be same]

$\frac{{kQ}_{A}}{R_{A}} = \frac{{kQ}_{B}}{R_{B}}$

as R_A > R_B

$∴$ Q_A > Q_B

_{$\frac{\frac{Q_{A}}{4 {πR}_{A}^{2}}}{\frac{Q_{B}}{4 {πR}_{B}^{2}}} = \frac{\frac{R_{A}}{R_{A}^{2}}}{\frac{R_{B}}{R_{B}^{2}}} = \frac{σ_{A}}{σ_{B}} = \frac{R_{B}}{R_{A}}$}

as R_A > R_B

$∴ σ_{B} > σ_{A}$

$∴$ E_B > E_A