A solid spherical conductor of radius 15 cm has a charge Q = 6.5 nC on it.A second,initially uncharged,spherical conductor of radius 10 cm is moved toward the first until they touch and is then moved far away from it.How much charge is there on the second sphere after the two spheres have been separated?
A)2.6 nC
B)2.2 nC
C)3.2 nC
D)3.9 nC
E)4.3 nC

Question

Quizplus · Accepted Answer

When two conductors touch, charge redistributes between them in proportion to their surface areas. The surface area of a sphere is given by $4\pi r^2$. The ratio of the surface areas (and thus the charge) for the two spheres is equal to the square of the ratio of their radii. Therefore, the charge on the second sphere after separation is $\frac{10^2}{(10^2 + 15^2)} \times 6.5 \, \text{nC} = \frac{100}{325} \times 6.5 \, \text{nC} = \frac{2}{5} \times 6.5 \, \text{nC} = 2.6 \, \text{nC}$.

A Solid Spherical Conductor of Radius 15 Cm Has a Charge