# Homework Help: Find direction of current in a magnetic field

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1. Oct 11, 2016

### moenste

1. The problem statement, all variables and given/known data
The diagram shows a uniform magnetic flux density B in the plane of the paper. Q and R mark the points where two long, straight and parallel wires carry the same current, I, in the same direction and perpendicular to the paper. The line through QR is at right angles to the direction of B.

P is a point where the resultant magnetic flux density is zero, i. e. it is a neutral point. P is closer to R than to Q.

(a) Explain whether the direction of the current I is into or out of the paper and sketch a diagram which shows the directions of the different magnetic flux densities present at P.

(b) If I is increased slightly, will the neutral point at P move towards Q or towards R?

(c) There is a second neutral point on the line through QR. State whether it is to the left of Q, between Q and R or to the right of R.

2. The attempt at a solution
(a) I have no idea how to find the direction of current. Boths wires are parallel and have one direction. How to find it?

This is how I see it.

(b) Nothing will change, right? Why would it?

Or maybe if the current is increased, the point will move towards R, towards the stronger wire? The P point is closer to R so I assume the field is stronger there. And we increase I, R the current at R will attract the P point even more. Maybe like this?

(c) Since both of the wires are the same, I would say that another point will be between Q and R, at the same distance from Q as P is from R. But not sure whether this is right.

Last edited: Oct 11, 2016
2. Oct 11, 2016

### Staff: Mentor

Only one direction of current will make it possible for the total B field at point P to be zero. Try each direction and see. (Hint: If you just consider the field from the wires alone, what direction is their resultant field?)

3. Oct 11, 2016

### moenste

I tried each direction, but it's just circles of field in one direction or the other.

4. Oct 11, 2016

### Staff: Mentor

Ask yourself: Which wire, Q or R, creates the greater field at point P? Thus: Which direction is the net field from the wires at point P? And then: Does that oppose or add to the given uniform field?

5. Oct 11, 2016

### moenste

I would say wire R should have a greater field at point P.

What does it mean? How can we calculate the net field?

6. Oct 11, 2016

### Staff: Mentor

Exactly.

Since you know that wire R creates a greater field than wire Q, what does that tell you about the direction of the net field due to the two wires?

(Hint: At point P, do the fields from wires Q and R point in the same or opposite direction?)

7. Oct 11, 2016

### moenste

I thought about from the start, but it is said that the wires have current in the same direction.

8. Oct 11, 2016

### Staff: Mentor

The current is in the same direction, but at point P are their fields in the same direction?

9. Oct 11, 2016

### moenste

They should be in different directions.

10. Oct 11, 2016

### Staff: Mentor

Exactly.

Now go back to my question:
Answer it for both cases: Current going into the page and current going out of the page.

11. Oct 11, 2016

### moenste

Out of paper: anti-clockwise (like R).

Into paper: clockwise (like R).

Like here:

12. Oct 11, 2016

### Staff: Mentor

Just answer my questions for point P. (It will be either "up" or "down" the page at that point.)

13. Oct 11, 2016

### moenste

If we are talking about the dimension of the image, then out of paper will be down and into paper will be up.

14. Oct 11, 2016

### Staff: Mentor

Good. And which is needed to get zero total field at P?

15. Oct 11, 2016

### moenste

Out of paper, because the field is already upwards?

16. Oct 11, 2016

### Staff: Mentor

Exactly. To cancel the upward uniform field, we need a downward field from the two wires.

17. Oct 11, 2016

### moenste

Alright, the (a) part looks logical now.

18. Oct 11, 2016

### Staff: Mentor

If the current increases, does the field from the wires increase or decrease at P? (How does the field from a wire depend on distance?)

19. Oct 11, 2016

### moenste

B = μ0 I / 2 π r? If we increase the current the field will also increase. If we increase the radius the field will decrease.

P should move closer to R?

20. Oct 11, 2016

### Staff: Mentor

Right. But that's for one wire. In between the two wires, the net field will be proportional to I (1/r1 - 1/r2).

Since I is increasing, P must move in whatever direction that makes (1/r1 - 1/r2) smaller.

21. Oct 11, 2016

### moenste

Uhm, but the question asks us to decide which point it should move to -- R or S. We can't answer that?

This should be solved using the same logic as in (a), right? I would say that the neutral point would be left to Q. This is where current around Q is facing downwards.

22. Oct 11, 2016

### Staff: Mentor

Sure you can answer it. Which direction -- towards Q or towards R -- makes the quantity I described in the last post get smaller (so as to counter the increased current)?

Right. Given that the current is out of the page and that we need the net field from the wires to point downward, the other neutral point must be to the left of Q.

23. Oct 11, 2016

### moenste

B = μ0 I / 2 π rQ - μ0 I / 2 π rR = 0, like this right? Since they both need to be equal to zero, if there is a neutral zone.

24. Oct 11, 2016

### Staff: Mentor

The field from the wires is not zero. (It has to be nonzero and directed opposite to that uniform field to get the total field equal to zero.)

25. Oct 11, 2016

### moenste

B = μ0 I / 2 π rQ + μ0 I / 2 π rR? So they should be summed up?

I think I don't get (b) at all. Could you maybe explain it once again? What is I (1 / r - 1 / r)? How do we know what r is larger or smaller?

By the way, if the currents are the same, as said in the problem, how come the R cable is stronger and attracts the P line?

Last edited: Oct 11, 2016