2) A short rectangular coil with 20 turns and sides of 30 cm and 50 cm has a res

Question

2) A short rectangular coil with 20 turns and sides of 30 cm and 50 cm has a resistance of 4 and the end of its last turn is electrically connected to the beginning of its first turn (the coil is short -circuited). The coil is initially in a region with a uniform magnetic field of 0.7 T, which is directed perpendicularly to the plane of the coil. Then within 0.3 s the direction of the magnetic field is reversed and its magnitude becomes 0.5 T. What is the average magnitude of current in the coil (in SI units) during these 0.3 sec?

A) 12 B) 3.0 C) 0.15 D) 1.75 E) 0.5

Explanation / Answer

The flux initially linking the coil, area A, is = NBA. After the rotation there is no flux linking the coil, so the flux change is then = NBA. The magnitude of the average induced voltage

Vind=t=IR=Rqt

where I is the average current and q is the total charge that flows. We see that q = /R and so:

q = NBA/R = 20 × 1.2T × 0.3m × 0.5m /4.0 = 0.9C

then current=q /t =0.9/0.3 =3 Amp (option (B))

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