Question 1

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 angular frequency of the current generated?

Accepted Answer

The angular frequency of the current generated in a spinning coil is equal to the angular velocity of the coil, which is given as 55 rad/s.

Question 2

A coil of wire rotates at a constant rate in a uniform magnetic field. Which of the following would NOT increase the induced current in the loop?

Accepted Answer

All of the options A, B, C, and D would increase the induced current according to Faraday's law of electromagnetic induction, which states that the induced electromotive force in a closed circuit is proportional to the rate of change of the magnetic flux through the circuit.

Question 3

A wire rod rolls with a speed of 30 m/s on two metallic rails, 2.0 m apart, that form a closed loop. The power dissipated in the resistor R and the current direction are, respectively,

Accepted Answer

The answer of  A wire rod rolls with a...

Question 4

A wire rod rolls with a speed of 20 m/s on two metallic rails, 1.0 m apart, that form a closed loop. If the magnetic field is 1.5 T into the page, the power dissipated in the resistor R and the current direction are, respectively,

Accepted Answer

The answer of  A wire rod rolls with a...

Question 5

A metal disk rotates about its central axis at an angular frequency of 800 radians per second in a uniform magnetic field of 0.8 T. The diameter of the disk is 8 cm. What is the magnitude of the voltage difference between the center and edge of the disk?

Accepted Answer

The voltage induced in a rotating metal disk in a magnetic field is given by:
$V = \frac{Bd^2\omega}{4}$

where B is the magnetic field, d is the diameter of the disk, and $\omega$ is the angular frequency. Plugging in the given values, we get:

$V = \frac{(0.8\ T)(0.08\ m)^2(800\ s^{-1})}{4} = 0.51\ V$

Therefore, the correct answer is C.

Question 6

2 V, then calculate the number of revolutions per second of the rod.

Accepted Answer

The answer of 2 V, then calculate the number of...

Question 7

A 0.8-m-long pole rotates about a perpendicular axis at one end. As the pole rotates, it passes through Earth's magnetic field, which has a perpendicular component of 3 × 10^-⁵T to the plane of rotation. If the pole rotates with a frequency of 5 revolutions per second, calculate the induced EMF across the ends of the pole.

Accepted Answer

The answer of  A 0.8-m-long pole rotates about a...

Question 8

What is the average induced EMF between the ends of the wings of a plane flying at a speed of 500 km/hr when the vertical component of Earth's magnetic field is 3 × 10^-⁵ T? The distance between the wingtips is 25 m.

Accepted Answer

The answer of What is the average induced EMF between...

Question 9

5 s, calculate the induced current in the loop if it is in series with a 20 ohm resistor.

Accepted Answer

The answer of 5 s, calculate the induced current in...

Question 10

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?

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.

Quiz 20: Electromagnetic Induction