Question about magnetic induction.

[Clara Chung]

Homework Statement

Homework Equations

The Attempt at a Solution

For cii), the answer is:
Yes. When the rod moves down, it moves across the horizontal field, cutting field lines. A current will be induced to oppose the motion. The magnetic force due to the motion is vertically upward.

But I think that, the voltage is induced in a direction perpendicular to the axis along PQ. No current can be formed. Therefore the rod will slide down as normal.

Why am I wrong? Thanks again.

 

[Simon Bridge]

Label the bottom two corners A and B ... A is below P and B is below Q.
By your reasoning, could there be a voltage induced between A and P?

If there were a voltage induced between P and Q, wouldn't the same voltage also be between A and B ... after all, these are conductors?

 

[Clara Chung]

Label the bottom two corners A and B ... A is below P and B is below Q.
By your reasoning, could there be a voltage induced between A and P?

If there were a voltage induced between P and Q, wouldn't the same voltage also be between A and B ... after all, these are conductors?

Yes, a voltage can be induced between A and P. However the same voltage is induced between B and Q. The situation will be just like a circuit with two batteries oppose to each other. Shouldn't there be no current?

 

[Clara Chung]

If there were a voltage induced between P and Q, wouldn't the same voltage also be between A and B ... after all, these are conductors?

I'm so sorry that I don't get your point, do you mean the situation in ci)?

 

[Simon Bridge]

When the magnetic field is vertical - you have no problem with there being a current along the rod between P and Q right?
Does that mean there is a voltage induced between P and Q?

 

[Clara Chung]

When the magnetic field is vertical - you have no problem with there being a current along the rod between P and Q right?
Does that mean there is a voltage induced between P and Q?

yes it does.

 

[Simon Bridge]

OK then - in that situation, would there be the same voltage between A and B?

 

[Clara Chung]

Sorry for asking stupid question. I think I now have problem with there being a current along the rod between P and Q. When a voltage is applied on PQ. That means PQAB is a short circuit. How do I account for the p.d. between AB?
By the way, there won't be induced emf on AB because it is not cutting any field lines.

 

[cnh1995]

By the way, there won't be induced emf on AB because it is not cutting any field lines.

Correct.

How do I account for the p.d. between AB?

That will depend on the resistances of the rod and the overall path, which are not given. The motional emf in the rod will be B*l*v, which will drive a current through the loop PQAB and ∫_{along loop PQAB}E.dl=dΦ/dt= B*l*v.

 

[Clara Chung]

Correct.

That will depend on the resistances of the rod and the overall path, which are not given. The motional emf in the rod will be B*l*v, which will drive a current through the loop PQAB and ∫_{along loop PQAB}E.dl=dΦ/dt= B*l*v.

Thanks and please take a look at the questions on #1 and #3.

 

[cnh1995]

But I think that, the voltage is induced in a direction perpendicular to the axis along PQ. No current can be formed. Therefore the rod will slide down as normal.

No. Apply the right hand rule and you'll see that an emf is induced in the rod along its length and it is equal to Blvsinθ, where θ is the angle between velocity vector and the magnetic field direction.

Yes, a voltage can be induced between A and P. However the same voltage is induced between B and Q. The situation will be just like a circuit with two batteries oppose to each other. Shouldn't there be no current?

This would be true if the entire loop PQAB were moving. In this problem, since only the rod PQ is moving, motional emf is induced only in the rod, which circulates a current in the loop.