Question

A uniform magnetic field B(t), pointing upward fills a circular region of radius, s in horizontal plane. If B is changing with time, find the induced electric field.

Answer 1

The area of the region, A = πs² , remains constant while B = B(f) is a function of time. Therefore, the induced emf,

[Note : Emf and electric field are different physical quantities, whose respective SI units are the volt and the volt per metre. The question has accordingly been corrected.]

[Hint : Part of Maxwell’s equation, applied to a time varying magnetic flux, leads us to the equation \(\oint \overrightarrow{E} .\overrightarrow{dl} =\cfrac{-d\phi_m}{dt},\) where \(\overrightarrow{E}\) is the electric field induced when the magnetic flux changes at the rate of \(\cfrac{d\phi}{dt}\)]