Question

A solid non conducting sphere of radius 1m carries a total charge of 10 C which is uniformly distributed throughout the sphere. Determine the charge density of the sphere.

(a) 10 C/m^3

(b) 4.76 C/m^3

(c) 0.1 C/m^3

(d) 2.38 C/m^3

I have been asked this question during an online interview.

This key question is from Continuous Charge Distribution topic in chapter Charges and Fields of Physics – Class 12

Answer 1

Correct answer is (d) 2.38 C/m^3

Best explanation: Volume of the sphere = \(\frac {4}{3}\)πr^3 where r is the radius of the sphere. Therefore, the charge density = \(\frac {total \, charge}{\frac {4}{3}\pi r^3}\). Now substituting the values, charge density = \(\frac {10}{\frac {4}{3}\pi r^3}\) = 2.38 C/m^3. But if the sphere is conducting, we have to consider the surface charge density.