Force in a magnetic field on a moving coil

[subhradeep mahata]

Homework Statement

A square coil (sorry, its not "current carrying" as shown in diagram, my mistake) of length L is released from rest, in a horizontal uniform magnetic field going into the plane of paper, of length 2L. What can you say about the coil's acceleration?

Homework Equations

The Attempt at a Solution

I am assuming that there is no friction involved. I also know that no force is exerted by a uniform magnetic field on a moving coil. So, my answer is that it remains equal to g all the time.
But the correct answer given is "equal to g when inside the magnetic field and less than g before going in and after coming out of the magnetic field. Can you explain me the reason behind it?

 

[Merlin3189]

Look at the amount of magnetic flux through the coil at each position as it falls.
Is the flux changing?
Will a current be induced?
What effect will this have on the coil's motion?

 

[subhradeep mahata]

@Merlin3189 That's a really good point you figured out. I will put forward my thoughts in accordance with the cases you provided.
1) nothing
2)nothing
3) Flux will change, as the coil is just entering the field region. Due to this, a current(due to motional emf) will be set up, in the anticlockwise current according to Lenz's law.
4) Flux is not changing, so no current
5) same as (4), no current induced
6) Flux changes, current induced in clockwise direction.
7-8) nothing
Now, I am not really sure how current induced/not induced will affect its motion.

 

[subhradeep mahata]

@Merlin3189 I also found out this:
just as the coil is entering the field region(case 3), the coil will experience a force due to magnetic field upwards (since current is anticlockwise). Also, as it is just leaving the field, it experiences a force upwards the current being clockwise. So, i guess that's the reason for it.
Just one extra question: as in case 3, only a part of the coil is inside the field, the rest of the coil is outside. So, is the current really going to flow throughout the coil?

 

[Merlin3189]

@Merlin3189 I also found out this:
just as the coil is entering the field region(case 3), the coil will experience a force due to magnetic field upwards (since current is anticlockwise). Also, as it is just leaving the field, it experiences a force upwards the current being clockwise. So, i guess that's the reason for it.

Yes. But you don't even need to go that far into the details. Lenz says that the induced current will oppose the change of flux, so the force caused by this current will oppose the movement causing the change of flux.

Just one extra question: as in case 3, only a part of the coil is inside the field, the rest of the coil is outside. So, is the current really going to flow throughout the coil?

The only place the current can flow is round the whole coil. The emf and induced current is determined by the change in total flux through the coil.
A certain flux through half the coil is the same as half the flux through the whole coil.
As the coil enters the field, it goes from no flux in the coil outside to the uniform field through the whole coil inside. Between these two points the flux is increasing. Once inside, the flux remains constant until the coil starts to leave the area of uniform field.

 

[subhradeep mahata]

Okay, got it. Thanks.