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For a uniformly charged thin spherical shell, the electric potential V measured radially away from the centre O of the shell can be graphically represented as [the shell has radius R, and the point A lies outside at a distance r from O]

Asked in JEE Main 6th April 1st Shift 2023 · Equipotential surfaces and V-r graphs

• (1) V grows from zero as a rising curve up to a peak at r=R and then falls linearly to zero
• (2) V rises linearly from zero to a peak at r=R and then falls off as 1/r
• (3) V is constant from the centre out to r=R and then falls off as 1/r
• (4) V is constant from the centre out to r=R and then falls linearly to zero

Step-by-step solution

Why the other options are wrong

• (1) Takes V to be zero at the centre, but the field inside is zero, so no work is needed to cross the cavity and V cannot change there.
• (2) A linear rise inside is the potential graph of a uniformly charged SOLID sphere misremembered; for a shell the interior is field free and the potential is flat.
• (4) Gets the flat interior right but then uses a straight line outside. Outside a shell the charge acts as a point charge, so V∝1/r, a hyperbola, not a straight line.

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