# The flux of magnetic field through a closed conducing ϕ = at2 + bt + c.(a) Writer the S.I. units of a, b and c.(b) If the magnitudes of a, b, and c are 0.20, 0.40 and 0.60 respectively, find the induced emf at t = 2s.

Given:

flux of magnetic field ϕ = at2 + bt + c

magnitudes of a, b and c= 0.20,0.40 and 0.60

(a) We know that,

Dimensions on both sides of an equation are equal and only terms with same dimensions can be added

Therefore

Dimensions of ϕ, at2, bt and c are same

Thus units of a are given by Now,

by faraday’s law of electromagnetic induction …(i)

Where

ϵ =emf produced

ϕ =flux of magnetic field

therefore, units of is same as voltage i.e. Volt Unit of b is given by Using eqn.(i) SI unit of c is given by  (b)

We know that

by faraday’s law of electromagnetic induction Where

ϵ =emf produced

ϕ =flux of magnetic field

here ϵ is given by Putting the values of a, b and t=2sec we have Therefore, the induced emf at t=2sec is given by 1.2Volts

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