Question

It is observed that N number of field lines come out perpendicularly from the unit surface area of the sphere. What is the amount of charge inside the sphere? ∈ is the dielectric constant of the medium.

(a) -4πR^2 N∈

(b) 4πR^2 N∈

(c) \(\frac {4\pi R^2}{N\epsilon}\)

(d) –\(\frac {4\pi R^2N}{\epsilon}\)

I had been asked this question by my college professor while I was bunking the class.

My question comes from Electric Field Lines in portion Charges and Fields of Physics – Class 12

Answer 1

The correct answer is (b) 4πR^2 N∈

Easy explanation: Field lines come out from the surface. That means the charge must be positive. According to Maxwell’s principle, field lines coming out from a charge q is equal to \(\frac {q}{\epsilon}\) where ∈ is the relative permittivity. The total number of field lines coming out of the sphere is 4πR^2N. This must be equal to \(\frac {q}{\epsilon}\). Therefore q=\(\frac {4\pi R^2}{N\epsilon}\).