# T/F Loop of a Wire Entering and exiting a field

1. Feb 19, 2014

### blue_lilly

1. The problem statement, all variables and given/known data
A square loop of wire with a small resistance is moved with constant speed from a field free region into a region of uniform B field (B is constant in time) and then back into a field free region to the left. The self inductance of the loop is negligible

In case my image doesn't load, this is the image that mine picture looks like.

True/False
1) Upon entering the field, a clockwise current flows in the loop.
2) Upon leaving the field, a counterclockwise current flows in the loop.
3) When entering the field the coil experiences a magnetic force to the right.
4) When leaving the field the coil experiences a magnetic force to the left.

2. Relevant equations
Right Hand Rule

Lenz Law- induced emf resulting from a changing magnetic flux has a direction that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change
Steps:
A) What is the direction of the field?
B) Is the flux getting bigger or weaker?
C) Induced Field: bolster or reduce?
D) What current is needed to get the induced field?

3. The attempt at a solution

I thought that
A)False -
1) direction of field: into the board
2) Flux is getting bigger
3) Induced field needs to reduce
4) Clockwise current is needed

B)True -
1) direction of field: into the board
2) Flux is getting smaller
3) Induced field needs to be bolstered
4) Counter Clockwise current is needed

C)False -
B-direction of field: into the board
V- velocity: left
F- magnetic force: down

D)False -
B- direction of field: into the board
V- velocity: left
F- magnetic force: down

I am not sure which parts, if any, are right and wrong. I am also not sure if I am using the right "way" (Lenz Law, right hand rule) to solve the problem.

Any help/explanation would be greatly appreciated!

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2. Feb 19, 2014

### BvU

Don't understand your A) 3) Induced field needs to reduce ?

Also it is abit strange that B) would be found true if you find A false ...

3. Feb 19, 2014

### collinsmark

I agree with everything except for maybe the clockwise part.

What is the direction of the change in the original flux? What direction of flux would a clockwise current cause? What direction does the induced flux need to be?

There is another way to approach this problem:

There are three (connected) wire segments shown in the diagram. An emf will be induced in at least one of these segments. Which one(s) and what direction is the emf?

Would a counterclockwise current produce a flux into or out of the board? Which direction does it need to be?

In this case, on which wire segment is an emf induced? What direction is the emf?

That would be the case if an isolated [Edit: and positive] charge was moving to the left. But there are no isolated charges in this situation (as a matter of fact, everything has a neutral net charge).

Instead, there are current carrying wires (not individual charges). Of the three current carrying wire segments shown, at least one of them has has a force acting on it, caused by it having current and its being in the magnetic field. What is the direction of the force on each of the wire segments? What is the net force?

There is also an alternate way to approach this problem involving conservation of energy. You can use that to check your answer.

Same as above. The things moving through the field are current carrying wires, not charges. What is the direction of force on each segment, and what is the net force?

Last edited: Feb 19, 2014
4. Feb 19, 2014

### blue_lilly

So the change in direction of the original flux would be to the left because the object is moving to the left. Then if the current is clockwise, the flux would be moving to the right. But our object is moving to the left, so it would be the opposite, counter clockwise. Is that right?

A counter clockwise current would produce a flux out of the board and it needs to be into the board. And a clockwise current would produce a flux into the board, which is what the drawing depicts. So because we need to bolster the induced field, we need to go the same direction as the field, so the current needed is clockwise. Right?

When you say "three current carrying wires" do you mean the object, the magnetic field and the velocity?

5. Feb 19, 2014

### collinsmark

That's not quite what I meant.

I didn't mean "change in direction," but rather I meant "direction of the change."

The induced flux needs to oppose that direction.

The original flux is into the board as you already mentioned. And in the the case of the loop moving to the left the flux is increasing. That means the change in flux is also into the board (in this particular case).

(As a reminder, this is in response to part 2, by the way, "T/F: Upon leaving the field, a counterclockwise current flows in the loop." the OP's original answer to this was "True.").

The original field is into the board. So the flux is also into the board. But when the loop is moving to the right, the flux is decreasing. So what is the direction of the change in flux?

There is an important distinction in problems like these:
• Direction of the flux
• Direction of the change in the flux
are not the same things.

The induced current must be in such a direction as to cause a field that opposes the change in the original flux (regardless of the direction of the flux. The change is what gets opposed.)

I meant the loop itself. Three segments/sections of the loop are shown in the diagram. It is implied that there is a fourth section somewhere off to the right, but not shown in the figure.

The figure shows three sections of the loop: two horizontal sections and one vertical section.

6. Feb 20, 2014

### BvU

Well well, are we talking of a square loop here, that is entering the field and leaving it again -- as the wording of the original post suggests ? Or could it be that the loop is not square, but rectangular, with a current return that remains outside of the magnetic field ?

7. Feb 20, 2014

### blue_lilly

It is a rectangular box but i think the coils inside are circular. Here is the image we are given. http://s3.amazonaws.com/answer-board-image/c45ed282-2566-4bee-aa01-419a3bc4d859.gif

8. Feb 20, 2014

### collinsmark

Re-reading my previous responses, I think I worded something sloppily. Forgive me for this. I would like to clear it up now.

Before I talked about the "direction" of the flux, and the direction of the change of the flux. I could have chosen my words better.

Magnetic fields are vector fields. But "flux" is actually a scalar quantity (the dot product of the field and the surface vector). Before I said something like "the flux is pointing into the board," but that, technically, doesn't make much sense.

But fluxes can be positive or negative. So in that sense they have a "direction" in the +/- sense. Also, fluxes can be increasing or decreasing. That means the change in a flux can also have a direction in the +/- sense.

I just wanted to clear that up.

--------------

But my other advice holds. The induced induced flux will be such that it opposes the change in the original flux.

[Edit: Assuming the circuit is closed so current is allowed to flow. At the very least, and induced emf will be generated such that that if current were allowed to flow the induced emf would produce an induced flux that opposes the change of the original flux.]

Same thing again,

The induced induced flux -- not the change in the induced flux, but rather the induced flux itself -- will be such that it opposes the change in the original flux -- not the original flux itself but the change in the original flux.

Last edited: Feb 20, 2014