A flat,rectangular coil measuring 0.10 m by 0.20 m and containing 50 turns of wire is rotating at a constant speed of 100$\pi$ rad/s in a magnetic field of 0.20 T.The maximum EMF induced in this coil is approximately
A)1.0 V
B)10 V
C)63 V
D)44 V
E)0.13 V

Question

Quizplus · Accepted Answer

The EMF induced is given by Faraday’s law of electromagnetic induction as:

EMF = -N(dΦ/dt)

where N is the number of turns in the coil and Φ is the magnetic flux through the coil.

The magnetic flux through the coil is given by:

Φ = BAbcosθ

where A is the area of the coil and θ is the angle between the magnetic field and the normal to the coil.

In this case, A = 0.10 m × 0.20 m = 0.02 m2 and θ = 0o (since the coil is rotating perpendicular to the magnetic field).

The rate of change of the magnetic flux is given by:

dΦ/dt = B(A/T)cosθ

where T is the period of rotation of the coil.

Therefore, the EMF induced is:

EMF = -N(dΦ/dt) = -NBAωsinθ = NABω = (50)(0.20 T)(0.02 m2)(100π rad/s) = 63 V

So, the best choice is C, 63 V.

A Flat,rectangular Coil Measuring 0 π\piπ Rad/s in a Magnetic Field of 0

A Flat,rectangular Coil Measuring 0 $\pi$ Rad/s in a Magnetic Field of 0