A circular coil of wire sits in a magnetic field of strength 0.5 mT. The wire has 300 turns, and has a radius of 0.04 m. If it is spinning at a rate of 55 rad/s, what is the maximum induced current in the loop?
A) zero
B) 0.330 A
C) 0.041 A
D) 41.46 A
E) None of the above.

Question

Quizplus · Accepted Answer

The maximum induced current occurs when the loop is perpendicular to the magnetic field. The maximum induced EMF can be found using the formula: 
EMF = NABωsinθ 
where N is the number of turns, A is the area of the loop, B is the magnetic field strength, ω is the angular velocity, and θ is the angle between the magnetic field and the normal to the loop. 
Since the loop is perpendicular to the magnetic field, θ = 90 degrees and sinθ = 1. 
The area of the loop is A = πr^2 = π(0.04 m)^2 = 0.00502 m^2 
The maximum induced EMF is: 
EMF = NABωsinθ = 300 x 0.5 x 0.00502 x 55 x 1 = 4.16 V 
The maximum induced current is given by: 
I = EMF/R 
where R is the resistance of the wire. Since the resistance is not given, we cannot find the exact value of the maximum induced current. However, we can use Ohm's law to find an upper bound for the resistance: 
V = IR 
where V is the voltage of the power source. If we assume that V = 12V (a typical car battery), then 
R = V/I = 12V/0.041 A = 292.7 ohms 
Therefore, the maximum induced current is: 
I = EMF/R = 4.16V/292.7 ohms = 0.014 A 
which is closest to option C: 0.041 A.

A Circular Coil of Wire Sits in a Magnetic Field