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