Find direction of current in a magnetic field

In summary, The diagram shows a uniform magnetic flux density B in the plane of the paper. The points Q and R mark the location of two long, straight, and parallel wires carrying the same current I in the same direction, perpendicular to the paper. The line through QR is perpendicular to the direction of B. Point P is a neutral point where the resultant magnetic flux density is zero and is closer to R than Q. (a) The direction of the current I can be determined by considering the direction of the resultant field from the two wires at point P. The net field must be in the opposite direction of the uniform field to cancel it out, so the current must be flowing out of the paper. (b) If the current I is
  • #1
moenste
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Homework Statement


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.

4bb2108f924a.jpg


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?

9697cce90dfd.jpg


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.
 
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  • #2
moenste said:
(a) I have no idea how to find the direction of current. Boths wires are parallel and have one direction. How to find it?
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?)
 
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  • #3
Doc Al said:
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?)
I tried each direction, but it's just circles of field in one direction or the other.

proxy.php?image=http%3A%2F%2Fs06.radikal.ru%2Fi179%2F1610%2Fe1%2F9697cce90dfd.jpg
 
  • #4
moenste said:
I tried each direction, but it's just circles of field in one direction or the other.
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?
 
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  • #5
Doc Al said:
Ask yourself: Which wire, Q or R, creates the greater field at point P?
I would say wire R should have a greater field at point P.

Doc Al said:
Which direction is the net field from the wires at point P?
What does it mean? How can we calculate the net field?
 
  • #6
moenste said:
I would say wire R should have a greater field at point P.
Exactly.

moenste said:
What does it mean? How can we calculate the net field?
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?)
 
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  • #7
Doc Al said:
(Hint: At point P, do the fields from wires Q and R point in the same or opposite direction?)
I thought about from the start, but it is said that the wires have current in the same direction.
 
  • #8
moenste said:
I thought about from the start, but it is said that the wires have current in the same direction.
The current is in the same direction, but at point P are their fields in the same direction?
 
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  • #9
Doc Al said:
The current is in the same direction, but at point P are their fields in the same direction?
They should be in different directions.
 
  • #10
moenste said:
They should be in different directions.
Exactly.

Now go back to my question:
Doc Al said:
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?

Answer it for both cases: Current going into the page and current going out of the page.
 
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  • #11
Doc Al said:
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?
Out of paper: anti-clockwise (like R).

Into paper: clockwise (like R).

Like here:

Fproxy.php%3Fimage%3Dhttp%253A%252F%252Fs06.radikal.ru%252Fi179%252F1610%252Fe1%252F9697cce90dfd.jpg
 
  • #12
moenste said:
Out of paper: anti-clockwise (like R).

Into paper: clockwise (like R).
Just answer my questions for point P. (It will be either "up" or "down" the page at that point.)
 
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  • #13
Doc Al said:
Just answer my questions for point P. (It will be either "up" or "down" the page at that point.)
If we are talking about the dimension of the image, then out of paper will be down and into paper will be up.
 
  • #14
moenste said:
If we are talking about the dimension of the image, then out of paper will be down and into paper will be up.
Good. And which is needed to get zero total field at P?
 
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  • #15
Doc Al said:
Good. And which is needed to get zero total field at P?
Out of paper, because the field is already upwards?
 
  • #16
moenste said:
Out of paper, because the field is already upwards?
Exactly. To cancel the upward uniform field, we need a downward field from the two wires.
 
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  • #17
Doc Al said:
Exactly. To cancel the upward uniform field, we need a downward field from the two wires.
Alright, the (a) part looks logical now.

What about (b)?
moenste said:
(b) If I is increased slightly, will the neutral point at P move towards Q or towards R?
moenste said:
(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?
 
  • #18
moenste said:
What about (b)?
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?)
 
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  • #19
Doc Al said:
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?)
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
moenste said:
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.
Right. But that's for one wire. In between the two wires, the net field will be proportional to I (1/r1 - 1/r2).
moenste said:
P should move closer to R?
Since I is increasing, P must move in whatever direction that makes (1/r1 - 1/r2) smaller.
 
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  • #21
Doc Al said:
Since I is increasing, P must move in whatever direction that makes (1/r1 - 1/r2) smaller.
Uhm, but the question asks us to decide which point it should move to -- R or S. We can't answer that?

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

moenste said:
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.
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
Doc Al said:
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)?
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
moenste said:
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.
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.)
 
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  • #25
Doc Al said:
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.)
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?
 
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  • #26
moenste said:
B = μ0 I / 2 π rQ + μ0 I / 2 π rR? So they should be summed up?
To find the field from both wires, you need to add them up. And since those fields point in opposite directions (at point P), one of them gets a negative sign.

moenste said:
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?
That's the same as you wrote above. We know that P is closer to R, so we know that rQ > rR.

moenste said:
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?
P is just an arbitrary point that is closer to R. The field from R is stronger only because P is closer to R than to Q.
 
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  • #27
Doc Al said:
To find the field from both wires, you need to add them up. And since those fields point in opposite directions (at point P), one of them gets a negative sign.That's the same as you wrote above. We know that P is closer to R, so we know that rQ > rR.P is just an arbitrary point that is closer to R. The field from R is stronger only because P is closer to R than to Q.
B = μ0 I / 2 π rQ - μ0 I / 2 π rR.

I still don't get it what to do with it. We have this formula, we know that rQ is larger rR. If we increase the current the field increases.

Maybe if we increase the current P will get closer to R? The one which it is already close.

r = μ0 I / B 2 π

If we increase I, r will also increase. So if we increase I, both rQ and rR will increase?

B = (4 π * 10-7) * 11 / 2 π 0.8 - (4 π * 10-7) * 11 / 2 π 0.2 = 2.75 * 10-6 - 1.1 * 10-5 = -8.25 * 10-6 T.

Now I = 12 A and we know that rR = 4 rQ

-8.25 * 10-6 = (4 π * 10-7) * 12 / 2 π rQ - (4 π * 10-7) * 12 / 2 π 4 rQ

-8.25 * 10-6 = 2.4 * 10-6 / rQ - 6 * 10-7 / rQ

-8.25 * 10-6 = 1.8 * 10-6 / rQ

-8.25 * 10-6 rQ = 1.8 * 10-6

rQ = -0.22 m (was 0.8)
rR = 4 rQ = -0.88 m (was 0.2).

So we can say that increasing I pushes P towards Q. Right?
 
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  • #28
P is just a point. It doesn't get pulled or pushed.

Realize the distance between Q and R is fixed and it equals rQ + rR.

Do you understand that we want to make 1/rQ - 1/rR smaller in order to counter the increase in current?

Play with some numbers. Let rQ = 8 and rR = 2. Calculate the quantity above with those numbers. Now move 1 unit closer to Q. How do things change? Then compare to moving 1 unit closer to R.
 
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  • #29
Doc Al said:
Do you understand that we want to make 1/rQ - 1/rR smaller in order to counter the increase in current?
Not sure that I understand this part.

We have a formula B = μ0 I / 2 π r
If we increase I, then B is changing and r also is changing?

Doc Al said:
Play with some numbers. Let rQ = 8 and rR = 2. Calculate the quantity above with those numbers. Now move 1 unit closer to Q. How do things change? Then compare to moving 1 unit closer to R.
If we move closer to R then the final number is larger (more negative), than if we move closer to Q.
 
  • #30
moenste said:
Not sure that I understand this part.

We have a formula B = μ0 I / 2 π r
If we increase I, then B is changing and r also is changing?
When the current is increased, you need to also increase r if you want to keep the B constant.

But we have two wires to worry about. We're trying to find the point where the combined field from the wires cancels the uniform field. It used to be point P, but then they went and increased the current on us.

moenste said:
If we move closer to R then the final number is larger (more negative), than if we move closer to Q.
Good! So which direction will the new 'neutral point' be?
 
  • #31
Doc Al said:
When the current is increased, you need to also increase r if you want to keep the B constant.

But we have two wires to worry about. We're trying to find the point where the combined field from the wires cancels the uniform field. It used to be point P, but then they went and increased the current on us.
But you said that B doesn't equal to zero, and now you say that the combined field from the wires cancels the uniform field.

Doc Al said:
Good! So which direction will the new 'neutral point' be?
Closer to R?
 
  • #32
moenste said:
But you said that B doesn't equal to zero
The B from the two wires doesn't equal zero.
moenste said:
and now you say that the combined field from the wires cancels the uniform field.
That's right.

moenste said:
Closer to R?
Just the opposite. The field from the wires is proportional to I * (1/rQ - 1/rR). Since I is increasing, and we want B to remain the same, we need (1/rQ - 1/rR) to decrease.
 
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  • #33
Doc Al said:
Just the opposite. The field from the wires is proportional to I * (1/rQ - 1/rR). Since I is increasing, and we want B to remain the same, we need (1/rQ - 1/rR) to decrease.
1 / 0.8 - 1 / 0.2 = - 3.75

1 / 0.9 - 1 / 0.1 = -8.89

1 / 0.7 - 1 / 0.3 = -1.9.

If we want it to increase, we need to increase the distance from Q. Therefore P goes closer tto R.
 
  • #34
moenste said:
If we want it to increase, we need to increase the distance from Q. Therefore P goes closer tto R.
That's true, but we want that factor to decrease, not increase.
 
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  • #35
Doc Al said:
That's true, but we want that factor to decrease, not increase.
Thank you, I think somehow I got it.
 

1. How do you determine the direction of current in a magnetic field?

To determine the direction of current in a magnetic field, you can use the right-hand rule. Simply point your right thumb in the direction of the current and your fingers will curl in the direction of the magnetic field.

2. What factors affect the direction of current in a magnetic field?

The direction of current in a magnetic field is affected by the direction of the magnetic field, the strength of the magnetic field, and the orientation of the conductor or wire carrying the current.

3. How does the direction of current in a magnetic field affect the force on a wire?

The direction of current in a magnetic field determines the direction of the force on a wire. When the current is perpendicular to the magnetic field, the force will be at a right angle to both the current and the magnetic field.

4. Can the direction of current in a magnetic field be reversed?

Yes, the direction of current in a magnetic field can be reversed by changing the direction of the current or by reversing the direction of the magnetic field.

5. How does the direction of current in a magnetic field impact the operation of an electric motor?

The direction of current in a magnetic field is crucial for the operation of an electric motor. The interaction between the current and the magnetic field causes a force that creates rotational motion, allowing the motor to function.

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