Consider two metal spheres, sphere 1 having radius R_1 = 20 cm, and sphere 2 hav

Question

Consider two metal spheres, sphere 1 having radius R_1 = 20 cm, and sphere 2 having a radius R_2 = 10 cm, separated far away from one another by a large center-to-center distance of 10 m. The two are connected to each other by a thin wire that is broken open in the middle by a switch. Sphere 1 is initially charged to 5 nC, and sphere 2 is neutral. When the switch is connected, charge moves spontaneously from sphere 1 to sphere 2 until equilibrium is reached. How much charge will be on each sphere when equilibrium is attained? (Assume that the charge is uniformly distributed on their surfaces, and negligible charge remains on the connecting wire because it is so thin.)

Explanation / Answer

R1 = 20 cm

R2 = 10 cm

Initial charge on sphere 1, Q = 5 nC

when they are connected by a wire charge moves from sphere 1 to sphere 2 untill they attain same potentail.

let q1 and q2 are the two charges on the spheres after connectung with a wire.

so, q1 + q2 = 5 nC ---(1)

Apply, V1 = V2

k*q1/R1 = k*q2/R2

q1/20 = q2/20

q2 = 2*q1

from equation 1

q1 + 2*q1 = 5 nc

q1 = (5/3) nc

= 1.667 nC <<<<<<-----------Answer

q2 = 2*q1

= 2*1.667 nC

= 3.333 nC <<<<<<-----------Answer

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