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How much charge should be placed on a spherical shell of radius 25 cm to have a surface charge density of 3/π C m⁻²?

Asked in GSEB Board March 2023 · Shell and uniform solid sphere

• (1) 0.57 C
• (2) 0.75 C
• (3) 0.25 C
• (4) 0.5 C

Step-by-step solution

Why the other options are wrong

• (1) No calculation gives 0.57 C: it is the correct 0.75 with its digits swapped. Check: 4π(0.25)²×3/π=0.75.
• (3) No single slip gives 0.25 C from this density; it is the charge a density of 1/π C m⁻² would need, one third of the real value.
• (4) No single slip gives 0.5 C; it corresponds to a density of 2/π C m⁻². With 3/π C m⁻² the shell needs 0.75 C.

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