The flux of magnetic field through a closed conducting loop changes with time according to the equation- - at 2- bt - c- aWrite the SI units of a-b and c-bIf the magnitudes of a-b and c are 0-20-0-40 and 0-60 respectively- find the induced emf at t -2 s-

Here ϕ =at^2 +bt^2 +c (a)a= ( ϕ/t^2 )= [ ϕ/t/t ]+Volt/sec b= [ ϕ/t ]=volt c=[ϕ]=weber (b)E=d ϕ/dt =2at +b =2 × 0.2 × 2+0.4 (∵ a=0.2, b=0.4,c=0.6) =0.8 +0.4 (t= ...

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Byju's Answer

Standard XII

Physics

Magnetic Flux and Faraday's Law

The flux of m...

Question

The flux of magnetic field through a closed conducting loop changes with time according to the equation, $Φ = a t^{2} + b t + c$ . (a)Write the SI 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=2 s.

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Solution

Here $ϕ = a t^{2} + b t^{2} + c$

$(a) a = (\frac{ϕ}{t^{2}}) = [\frac{\frac{ϕ}{t}}{t}] + \frac{V o l t}{s e c}$

$b = [\frac{ϕ}{t}] = v o l t c = [ϕ] = w e b e r$

$(b) E = \frac{d ϕ}{d t}$

$= 2 a t + b = 2 \times 0.2 \times 2 + 0.4$

$(∵ a = 0.2, b = 0.4, c = 0.6)$

=0.8 +0.4 (t=2s)

=1.2 volt.

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The flux of magnetic field through a closed conducting loop changes with time according to the equation, Φ=at2+bt+c. (a)Write the SI 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=2 s.

Here ϕ=at2+bt2+c (a)a=(ϕt2)=[ϕtt]+Voltsec b=[ϕt]=voltc=[ϕ]=weber (b)E=dϕdt =2at+b=2×0.2×2+0.4 (∵a=0.2,b=0.4,c=0.6) =0.8 +0.4 (t=2s) =1.2 volt.

The flux of magnetic field through a closed conducting loop changes with time according to the equation, $Φ = a t^{2} + b t + c$ . (a)Write the SI 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=2 s.