A point charge of magnitude +1 is fixed at (0, 0, 0). An isolated… | JEE Main 2013 (22 Apr, Shift 1)

Q112JEE Main 2013 · 22 APR · SHIFT 1Medium

Electric Potential & Equipotentials

A point charge of magnitude $+1\,\mu\text{C}$ is fixed at (0, 0, 0). An isolated uncharged spherical conductor, is fixed with its center at (4, 0, 0). The potential and the induced electric field at the centre of the sphere is:

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Answer: (c)

Induced charges on the sphere total zero and all lie at distance $R$ from its centre, so they add no potential there.
$V = \dfrac{kq}{r}$ ; with $r = 4$ cm $= 0.04$ m: $V = \dfrac{9\times10^9\times10^{-6}}{0.04} = 2.25\times10^5$ V
Net field inside a conductor is zero, so induced field $= -\dfrac{kq}{r^2} = -\dfrac{9\times10^3}{(0.04)^2} = -5.625\times10^6$ V/m
So the answer is (c).

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Electric Potential & Equipotentials question from JEE Main 2013 (22 Apr, Shift 1)

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