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The total charge on a uniformly charged spherical shell having radius R is Q. Then electric potential at a distance r = R/2 from the centre of the shell __________.

Asked in GUJCET 2026 · Potential of shells and spheres

• (1) Q/(4πε₀R)
• (2) Q/(2πε₀R)
• (3) Q/(πε₀R)
• (4) Q/(8πε₀R)

Step-by-step solution

Why the other options are wrong

• (2) This uses the point-charge formula at r = R/2: Q/(4πε₀(R/2)) = Q/(2πε₀R), twice the surface value. That formula holds only outside the shell.
• (3) This scales the surface value by (R/r)² = 4, as if the potential fell off like 1/(r²) (that is how a point charge's field behaves, not its potential): 4×Q/(4πε₀R) = Q/(πε₀R).
• (4) This halves the surface value, as if the potential grew in proportion to r from zero at the centre. Inside the shell the field is zero, so the potential does not change at all between the centre and the surface.

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