A 37-turn circular coil of radius 4.60 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 = 4.20 s.
The area of a circular coil of radius r is .
Given the magnetic field passing through the coil is
The magnetic flux passing through area A in presence of uniform magnetic field B is
where the area vector is directed normal to the area, is the angle that the magnetic field makes with the area vector or with the normal of the area. Since the magnetic field is normal to the coil, the angle between them is zero. . The magnetic flux passing through a single turn of the coil is
There are 37 turns in the coil, the magnetic flux passing through the coil is
The magnitude of the emf induced in the coil is given by flux rule
Given radius is r=4.60cm=0.046m, and we want to find the induced emf at time t=4.20 seconds.
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