Q. 24.7( 3 Votes )

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.

Answer :


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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