Two metal spheres,one of radius R and the oth | vedclass

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(A) Initial charges on the spheres are $Q_1 = \sigma(4\pi R^2)$ and $Q_2 = \sigma(4\pi(2R)^2) = 16\pi R^2\sigma = 4Q_1$.Total charge $Q_{total} = Q_1

Vedclass · Accepted Answer

$\sigma_1 = \frac{5}{3}\sigma, \sigma_2 = \frac{5}{6}\sigma$

Vedclass · Answer

(A) Initial charges on the spheres are $Q_1 = \sigma(4\pi R^2)$ and $Q_2 = \sigma(4\pi(2R)^2) = 16\pi R^2\sigma = 4Q_1$.Total charge $Q_{total} = Q_1 + Q_2 = 5Q_1 = 20\pi R^2\sigma$.When brought in contact,they reach a common potential $V$. Since $V = \frac{kQ'}{r}$,we have $\frac{kQ_1'}{R} = \frac{kQ_2'}{2R}$,which implies $Q_2' = 2Q_1'$.Using conservation of charge: $Q_1' + Q_2' = 5Q_1 \implies 3Q_1' = 5Q_1 \implies Q_1' = \frac{5}{3}Q_1$ and $Q_2' = \frac{10}{3}Q_1$.New surface charge densities are $\sigma_1' = \frac{Q_1'}{4\pi R^2} = \frac{5/3(\sigma \cdot 4\pi R^2)}{4\pi R^2} = \frac{5}{3}\sigma$.$\sigma_2' = \frac{Q_2'}{4\pi(2R)^2} = \frac{10/3(\sigma \cdot 4\pi R^2)}{16\pi R^2} = \frac{10}{3} \cdot \frac{1}{4} \sigma = \frac{5}{6}\sigma$.

Two metal spheres,one of radius $R$ and the other of radius $2R$,both have the same surface charge density $\sigma$. They are brought in contact and then separated. What will be the new surface charge densities on them?

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