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A 23-turn circular coil of radius 3.40 cm and resistance 1.00 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.010 0t + 0.040 0t2, where B is in teslas and t is in seconds.

Calculate the induced emf in the coil at t = 5.40 s.

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Answer:

Emf will be [tex]36.8\times 10^{-3}volt[/tex]                

Explanation:

We have given number of turns N = 23

Radius of the coil r = 3.40 cm = 0.034 m

So area of the coil [tex]A=\pi r^2=3.14\times 0.034^2=0.00362m^2[/tex]

Magnetic field is given as [tex]B=0.01t+0.04t^2[/tex]

We have to find the emf at t = 5.4 sec

We know that emf is given by

[tex]e=A\frac{dB}{dt}=0.00362\times \frac{d(0.01t+0.04t^2)}{dt}[/tex]

[tex]e=NA\frac{dB}{dt}=0.00362\times(0.01+0.08t)[/tex]

So emf at t = 5.4 sec

[tex]e=23\times0.00362\times(0.01+0.08\times 5.4)=36.8\times 10^{-3}volt[/tex]

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