Question

How many electrons must be added to an isolated spherical conductor of radius 20cm to produce an electric field 1000N/C just outside the surface?

(a) 2.77*10^20

(b) 2.77*10^10

(c) 1.77*10^10

(d) 5.4*10^10

I have been asked this question at a job interview.

I'd like to ask this question from Continuous Charge Distribution topic in portion Charges and Fields of Physics – Class 12

Answer 1

Correct choice is (b) 2.77*10^10

The explanation is: The electric field E = k \(\frac {Q}{r^2}\) where k=9*10^9 N m^2 C^-2 and Q is the charge of the sphere, r is the radius of the sphere. Therefore Q = \(\frac {E*r^2}{k}=\frac {1000*0.2^2}{9*10^9}\) = 4.44*10^-9. Number of electrons required for this amount of charge is = \(\frac {4.44*10^{-9}}{1.602*10^{-19}}\) = 2.77*10^10.