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Two hollow concentric conducting spheres of radii 2 cm and 4 cm carry charges of 2 C and 4 C respectively. Find the ratio of the total charge on the outer surface of the outer sphere before connecting the two spheres to that after they are joined by a conducting wire.

1. 1
2. 2/3
3. infinity
4. 0

Correct answer: 1

Solution

For any conductor system, the charge appearing on the outermost surface equals the algebraic sum of all enclosed charges = total charge. Before connection, the outer surface of the outer sphere carries 2 + 4 = 6 C. After connecting with a wire, the inner sphere's charge flows to the outer sphere, but the total is still 6 C, so the outermost surface still carries 6 C. The ratio is 6/6 = 1.

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