A charge is placed on a spherical conductor of radius r₁.This sphere is then connected to a distant sphere of radius r₂ (not equal to r₁)by a conducting wire.After the charges on the spheres are in equilibrium, A)the electric fields at the surfaces of the two spheres are equal. B)the amount of charge on each sphere is q/2. C)both spheres are at the same potential. D)the potentials are in the ratio $\frac { V _ { 2 } } { V _ { 1 } } = \frac { q _ { 2 } } { q _ { 1 } }$ . E)the potentials are in the ratio $\frac { V _ { 2 } } { V _ { 1 } } = \frac { r _ { 2 } } { r _ { 1 } }$ .

Question

Quizplus · Accepted Answer

When the two spheres are connected by a conducting wire, the charges on the spheres will redistribute until they reach equilibrium. At equilibrium, the potential on the two spheres will be equal since they are connected by a wire (otherwise there would be a potential difference and charges would continue to flow until equilibrium is reached). Therefore, both spheres are at the same potential, making choice C the correct answer. The electric fields at the surfaces of the two spheres may be different depending on the charges and radii of the spheres, so choice A is incorrect. The amount of charge on each sphere cannot be determined without knowing the charges and radii of the spheres, so choice B is incorrect. The potentials are not in the ratio given in choices D and E, as there is no reason to expect this to be true without further information.

A Charge Is Placed on a Spherical Conductor of Radius V2V1=q2q1\frac { V _ { 2 } } { V _ { 1 } } = \frac { q _ { 2 } } { q _ { 1 } }V1​V2​​=q1​q2​​

A Charge Is Placed on a Spherical Conductor of Radius $\frac { V _ { 2 } } { V _ { 1 } } = \frac { q _ { 2 } } { q _ { 1 } }$