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Two uniformly charged spherical conductors, A and B, have radii 1 mm and 2 mm respectively and are kept 5 cm apart. If the two spheres are joined by a conducting wire, then at electrostatic equilibrium the ratio of the magnitudes of the electric fields just outside the surfaces of A and B is

1. 4: 1
2. 1: 2
3. 2: 1
4. 1: 4

Correct answer: 2: 1

Solution

After joining, both spheres reach the same potential V = kQ/r, and the surface field is E = V/r. With equal V, E is proportional to 1/r, so E_A/E_B = r_B/r_A = 2/1. The ratio is 2:1.

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