What is the net force on the current loop?

[Meow12]

Homework Statement

A rectangular current loop carrying $10A$ is near a long wire carrying
$5A$ with the geometry indicated in the figure. What is the magnitude and direction of the net force on the current loop?

Relevant Equations

$\vec B=-\frac{\mu_0I}{2\pi x}$ into the page

$\vec{F}=\int I\vec{dl}\times\vec{B}$

The long wire carrying $5A$ current causes a non-uniform magnetic field whose formula is known. I calculated the force exerted by this magnetic field on each of the four sides of the rectangular loop and summed them up. I got the right answer, but a question is nagging me---doesn't the loop carrying $10 A$ current also create a magnetic field?

 

[BvU]

Hi,

It certainly does. But what about the net force it causes on the current loop ?

$\$

 

[Meow12]

Hi,

It certainly does. But what about the net force it causes on the current loop ?

$\$

Is it zero? Because an object can never exert a net force on itself?

 

[BvU]

It is zero. I'm not so certain about the why (I can stand up from a sitting position...).

$\$

 

[kuruman]

I got the right answer, but a question is nagging me---doesn't the loop carrying $10 A$ current also create a magnetic field?

It sure does and you can use Biot-Savart to find what it is at an arbitrary point in space. Why is that nagging you?

 

[Meow12]

It sure does and you can use Biot-Savart to find what it is at an arbitrary point in space. Why is that nagging you?

I had thought that a side of the rectangular loop may experience forces due to the magnetic fields created by the other three sides of the loop. But I think these internal forces will cancel.

 

[kuruman]

Right. However, all four sides of the loop exert magnetic forces on the long wire and you can easily figure out the net force on the long wire due to the current loop.

 

[kuruman]

It is zero. I'm not so certain about the why (I can stand up from a sitting position...).

Try pulling up on your collar and see if you can stand up from a sitting position.

 

[Orodruin]

It is zero. I'm not so certain about the why (I can stand up from a sitting position...).

Although not by exerting a net force on yourself (it is by exerting a force larger than your weight on the chair).