How much charge is on a conducting sphere of diameter 20 $\mu$m if its surface potential is at 50 mV?

Question

Quizplus · Accepted Answer

The charge Q on a conducting sphere is given by

Q = 4πεrV

where ε is the permittivity of free space, r is the radius of the sphere (half the diameter), and V is the surface potential.

First, we need to convert the diameter to radius:

r = 20 μm / 2 = 10 μm

Then we can calculate the charge:

Q = 4π(8.85 x 10^-12 F/m)(10 x 10^-6 m)(50 x 10^-3 V) 
  = 5.6 x 10^-18 C

Converting to scientific notation:

Q = 56 x 10^-19 C

So the best choice is B.

How Much Charge Is on a Conducting Sphere of Diameter μ\muμ