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9. A magnetic field is perpendicular to the plane of a single-turn circular coil

ID: 1874481 • Letter: 9

Question

9. A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of the field is changing, so that an emf of 0.58 V and a current of 2.6 A are induced in the coil. The wire is then re-formed into a single-turn square coil, which is used in the same magnetic field (again perpendicular to the plane of the coil and with a magnitude changing at the same rate). What emf is induced in the square coil? 10. A rectangular loop of wire (width W=7.00 cm) is moving as shown in the drawing with a speed of 2.30 m/s. The loop is leaving a region in which a 2.2 T magnetic field exists; the magnetic field outside this region is zero. During a time of 0.10 s, what is the magnitude of the change in the magnetic flux?

Explanation / Answer

induced emf, e = d(flux)/dt = A dB/dt

e / A = dB/dt = constant

suppose initially radius was r.

then length of wire= 2 pi r

when formed into wire, 4L = 2pi r

A = pi r^2

A' = L^2 = pi^2 r^2 /4

e /A = e' / A'

0.58 / (pi r^2) = e'/ ( pi^2 r^2 / 4)

e' = 0.46 Volt

10. rate change in flux = B dA/dt

A = W L and dA/dt =w dL/dt = w v

rate of change in flux = B w v = 2.2 x 0.07 x 2.30

= 0.3542 Wb/s

change in flux = 0.3524 x 0.10 = 0.035 Wb