Induced EMF and circular coil

[Darth Geek]

Homework Statement

A circular coil, with radius of 10 cm, and 25 turns, rotates in a constant magnetic field of
strength 2.4 T, with the axis of rotation perpendicular to the direction of the magnetic
field.

(a question about finding the induced voltage- 5.92 V)

part C. If the magnetic field that the coil is in points down the page, which direction
does the coil rotate? Answer for both cases: (1) q traveling from left to right
and (2) q traveling from right to left in the coil. (Draw a diagram to help you.)

Homework Equations

Torque on a loop of wire in a magnetic field: τ = I · A · B · sinθ

Magnetic flux: φ = B · A · cosθ

Induced potential difference (emf)
due to a changing magnetic field: V = -N · ∆φ/∆t

The Attempt at a Solution

I really have no idea how to start this one, since the oh-so helpful Apex (Not) Learning doesn't give me any information about this, instead restating essentially the same Faraday's Law problem throughout the 'notes'. I'm not even sure my original answer concerning the voltage is correct, since there is no area facing the B-field and therefore negligible flux.

I've thought of using the Lorentz Force and saying that the loop rotates out of the page, but the problem seems to imply that it is (counter)clockwise in the page.

 

[Andrew Mason]

Homework Statement

A circular coil, with radius of 10 cm, and 25 turns, rotates in a constant magnetic field of
strength 2.4 T, with the axis of rotation perpendicular to the direction of the magnetic
field.

(a question about finding the induced voltage- 5.92 V)

part C. If the magnetic field that the coil is in points down the page, which direction
does the coil rotate? Answer for both cases: (1) q traveling from left to right
and (2) q traveling from right to left in the coil. (Draw a diagram to help you.)

Homework Equations

Torque on a loop of wire in a magnetic field: τ = I · A · B · sinθ

Magnetic flux: φ = B · A · cosθ

Induced potential difference (emf)
due to a changing magnetic field: V = -N · ∆φ/∆t

The Attempt at a Solution

I really have no idea how to start this one, since the oh-so helpful Apex (Not) Learning doesn't give me any information about this, instead restating essentially the same Faraday's Law problem throughout the 'notes'. I'm not even sure my original answer concerning the voltage is correct, since there is no area facing the B-field and therefore negligible flux.

I've thought of using the Lorentz Force and saying that the loop rotates out of the page, but the problem seems to imply that it is (counter)clockwise in the page.

This is a Lorentz force problem for a current carrying conductor in a magnetic field. You can use the right hand rule or you can work it out: The Lorentz force is a cross product of what two vectors? Take a small length of the coil 90 deg. from the axis. What is the direction of the cross product vector? Then take a small section of the coil diametrically opposite. What is the direction of the Lorentz force? That will tell you how it will rotate.

AM

 

[baba89]

I'm also not sure if the coil rotates at all, since the problem only asks for the direction, not the magnitude of the rotation.

In situations like this, it is important to carefully read the problem statement and identify what information is given and what is being asked. In this case, we are given the radius, number of turns, and strength of the magnetic field, and we are asked about the direction of rotation and the induced voltage.

To start, we can use the equation for the torque on a loop of wire in a magnetic field to determine the direction of rotation. Since the axis of rotation is perpendicular to the magnetic field, the angle between the magnetic field and the area vector of the coil (θ) is 90 degrees. This means that the torque will be maximum, and the direction of rotation will be determined by the direction of the current in the coil.

Using the right-hand rule, we can determine that if the current is traveling from left to right in the coil, the torque will cause the coil to rotate clockwise in the page. If the current is traveling from right to left, the torque will cause the coil to rotate counterclockwise in the page.

Next, to determine the induced voltage, we can use Faraday's Law which states that the induced emf is equal to the negative rate of change of magnetic flux. In this case, since the coil is rotating in a constant magnetic field, the flux is not changing and therefore the induced voltage will be zero. This makes sense since, as you mentioned, there is no area facing the magnetic field and therefore no change in flux.

In summary, the direction of rotation will depend on the direction of the current in the coil, and the induced voltage will be zero. It is important to carefully read the problem and use the appropriate equations and concepts to solve it.