Consider two isolated metal spheres,the first with a charge of 8.7 and a radius of 25 cm and the second uncharged with a radius of 5.4 cm.What is the charge on the larger sphere after a long thin metal wire is used to connect the two spheres?

Question

Consider two isolated metal spheres,the first with a charge of 8.7  and a radius of 25 cm and the second uncharged with a radius of 5.4 cm.What is the charge on the larger sphere after a long thin metal wire is used to connect the two spheres?

Quizplus · Accepted Answer

When the two spheres are connected by the wire, the charge on the larger sphere will distribute itself between the two spheres such that both spheres will have the same potential. Since the spheres are isolated, charge is conserved. Let Q be the final charge on the larger sphere. Then, using the principle of conservation of charge, we have:

Qinitial = Qfinal = Q

Since the smaller sphere is initially uncharged, its potential is 0. Therefore, the potential of the larger sphere after being connected to the smaller sphere is also 0. We can use the formula for the potential of a conducting sphere to derive the final charge on the larger sphere:

V = kQ/r

where V is the potential, k is Coulomb's constant, Q is the charge, and r is the radius of the sphere.

For the smaller sphere, we have:

0 = kQ/5.4

For the larger sphere, we have:

0 = kQ/25

Equating the two, we get:

kQ/5.4 = kQ/25

Solving for Q, we get:

Q = 7.2 x 10^-9 C

Therefore, the final charge on the larger sphere is 7.2 nC. The answer is D.

Consider Two Isolated Metal Spheres,the First with a Charge of 8.7