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Physics · PYQ NEET UG 2019(2)
हिन्दीTwo metal spheres, one of radius \( R \) and the other of radius \( 2R \) respectively have the same surface charge density \( \sigma \). They are brought in contact and separated. What will be the new surface charge densities on them?
Correct answer · Option 1
\( \sigma_1 = \frac{5}{3}\sigma, \sigma_2 = \frac{5}{6}\sigma \)
Explanation
Total charge \( Q = \sigma(4\pi R^2) + \sigma(4\pi (2R)^2) = 20\pi R^2 \sigma \). After contact, potentials are equal: \( V_1 = V_2 \). New charges are proportional to radii: \( q_1 = \frac{R}{R+2R}Q = \frac{1}{3}Q \), \( q_2 = \frac{2}{3}Q \). New surface densities \( \sigma_1 = \frac{q_1}{4\pi R^2} = \frac{5}{3}\sigma \) and \( \sigma_2 = \frac{q_2}{4\pi (2R)^2} = \frac{5}{6}\sigma \).
