# Force from a Current in an Infinite Wire on a Square Wire Loop Nearby

• Schfra
In summary: Then think about the force on the top side of the loop and the right side of the loop. Then add up the three forces to get the net force on the loop.In summary, the conversation discusses a problem involving a horizontal infinite straight wire with current I1 and a square horizontal loop with current I2. The question asks for a qualitative explanation of why the force on the square points to the left, and then to show that the net force equals μ0I1I2l2/2πR2, where R = z2 + (l/2)2 is the distance from the wire to the right and left sides of the square. This is done by analyzing the magnetic force on different parts of the loop and
Schfra

## Homework Statement

Figure 6.47 shows a horizontal infinite straight wire with current I1 pointing into the page, passing a height z above a square horizontal loop with side length l and current I2. Two of the sides of the square are parallel to the wire. As with a circular ring, this square produces a magnetic field that points upward on its axis. The field fans out away from the axis. From the right-hand rule, you can show that the magnetic force on the straight wire points to the right. By Newton’s third law, the magnetic force on the square must therefore point to the left.
Your tasks: explain qualitatively, by drawing the fields and
forces, why the force on the square does indeed point to the left;
then show that the net force equals μ0I1I2l2/2πR2, where R =
z2 + (l/2)2 is the distance from the wire to the right and left sides of the square. (The calculation of the force on the wire is a bit more involved. We’ll save that for Exercise 11.20, after we’ve discussed magnetic dipoles.)

B = uI/(2piR)

## The Attempt at a Solution

I’m not quite sure where to start on this one. The first part of the question is a bit confusing, what do they want me to do? It seems like they already explained why the force on the square points left. Should I just draw a picture of what they already explained?

#### Attachments

• 7050420D-243D-4E47-88BF-2375C8DD0FE5.jpeg
5 KB · Views: 540
Last edited by a moderator:
They used Newton's 3rd law to conclude that the force on the loop is to the left. But they want you to verify this by analyzing the magnetic force on various parts of the loop to show that the net magnetic force on the loop is to the left (without using the 3rd law).

Your expression for the force is μ0I1I2l2/2πR2. It would be helpful if you used the subscript and superscript tools on the toolbar to write this more legibly.

#### Attachments

• upload_2018-4-10_11-50-32.png
1.7 KB · Views: 991
Last edited:
Schfra
TSny said:
They used Newton's 3rd law to conclude that the force on the loop is to the left. But they want you to verify this by analyzing the magnetic force on various parts of the loop to show that the net magnetic force on the loop is to the left (without using the 3rd law).

Your expression for the force is μ0I1I2l2/2πR2. It would be helpful if you used the subscript and superscript tools on the toolbar to write this more legibly.
View attachment 223748
Sorry, that force is μ0I1I2L2/2πR2.

How do I know how the magnetic field affects the square? I’m only familiar with finding the effects of magnetic fields on moving charges.

Schfra
Schfra said:
But that formula doesn’t tell us about how the square reacts to the magnetic field from the wire does it? And isn’t the force acting on the square what I need to find?
Yes, you need to find the force on the square. The wire that carries a current ##I_1## produces a magnetic field around it. The square loop sits in this magnetic field. So, this magnetic field will exert a magnetic force on the current in the loop. You might start with the left side of the loop (where the current is coming out toward you) and think qualitatively (right-hand-rule) about the direction of the magnetic force on this side of the loop. You will need to think about the direction of the magnetic field (producued by ##I_1##) at this side of the loop.

## 1. What is the force from a current in an infinite wire on a square wire loop nearby?

The force from a current in an infinite wire on a square wire loop nearby is known as the Ampere's force. It is the force exerted on a conductor by a magnetic field created by a current-carrying wire.

## 2. How does the magnitude of the current affect the force on the wire loop?

The magnitude of the current in the infinite wire is directly proportional to the force on the wire loop. This means that as the current increases, the force on the wire loop also increases.

## 3. What is the direction of the force on the wire loop?

The direction of the force on the wire loop is perpendicular to both the current in the infinite wire and the loop itself. This is known as the right-hand rule, where the thumb points in the direction of the current and the fingers point in the direction of the force.

## 4. How does the distance between the infinite wire and the wire loop affect the force?

The force on the wire loop is inversely proportional to the distance between the infinite wire and the loop. This means that as the distance increases, the force decreases and vice versa.

## 5. Does the orientation of the wire loop affect the force from the current in the infinite wire?

Yes, the orientation of the wire loop does affect the force from the current in the infinite wire. If the loop is parallel to the infinite wire, there will be no force. However, if the loop is perpendicular to the infinite wire, there will be a maximum force.

Replies
4
Views
1K
Replies
8
Views
780
Replies
4
Views
587
Replies
3
Views
628
Replies
17
Views
2K
Replies
2
Views
1K
Replies
1
Views
275
Replies
9
Views
2K
Replies
3
Views
1K
Replies
12
Views
1K