# 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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