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Question

An insulated sphere of radius R has a volume charge density ρ . The variation of its potential with respect to the distance from the centre is best represented by

A
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B
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C
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D
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Solution

The correct option is A
The variation of electric potential due to a uniformly charged sphere (one with volume charge density)
with distance from the centre is given by
V=kQ2R(3r2R2)for r<RkQr for r>R
If you don’t know this and are wondering “How on earth am I supposed to know that?” then I strongly recommend you to go through the derivation video for ‘Electric potential due to uniformly charged spherical distribution’ Now we have for r<R,V=KQ2R (3r2R2) this is an equation of an inverted parabola (a quadratic in r) if we put r=0, we get V=3KQr we now know that the graph doesn’t start from (0,0) but (0,3KQ2R) option (b) and (c) is obviously incorrect.
and when r>R, we have V=KQr is a hyperbolic curve. The graph will shift to hyperbola at r=R. Option (d) is a single curve. Option (a) is correct.

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