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A hollow metal sphere of radius 10 cm is charged such that the potential on its surface becomes 80 V. The potential at the centre of the sphere is ______.

Asked in GUJCET 2011 · Potential of shells and spheres

• (1) 80 V
• (2) 800 V
• (3) 8 V
• (4) Zero

Step-by-step solution

Why the other options are wrong

• (2) This divides the potential by the radius: (80)/(0.1) = 800. That is the field just outside the surface, in V m⁻¹, not a potential.
• (3) This multiplies the potential by the radius: 80×0.1 = 8. That product has units of V m and means nothing here.
• (4) It is the field inside the sphere that is zero, not the potential. Zero field means the potential does not change inside, so it keeps the surface value.

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