A metal sphere with radius r a = 1.20 cm is supported on an insulating stand at

Question

A metal sphere with radius ra = 1.20 cm is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb = 9.10 cm . Charge +q is put on the inner sphere and charge q on the outer spherical shell. The magnitude of q is chosen to make the potential difference between the spheres 400 V , with the inner sphere at higher potential.

Part A:Calculate q

Part B:

Are the electric field lines and equipotential surfaces mutually perpendicular?

Part C:

Are the equipotential surfaces closer together when the magnitude of E is largest?

Explanation / Answer

a) V = k q / ra - k q / rb

400 = 8.99 * 109 * q [1 / 0.012 - 1/0.091]

q = [400 / 8.99 * 109] / [1 / 0.012 - 1/0.091]

q = 6.14 * 10-10 C

b) YES, electric field lines and equipotential surfaces are mutually perpendicular

c) Equipotential surfaces closer together when the magnitude of E is largest

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