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

It is observed that N number of field lines come out perpendicularly f

1.	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» 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=\(\frac {4\pi R^2}{N\epsilon}\).

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