Understanding Torque in a Metal Coil with Magnetic Field

[anonymousphys]

Homework Statement

For a metal coil, if a magnetic field is being applied parallel to each circular loop, why is there torque being exerted on the coil?

Homework Equations

torque=(magnetic field)(area)(current)

The Attempt at a Solution

When I cross the current with the magnetic field, I get a vector pointing down the coil. Isn't this a compression of the coil instead of a rotation? How is there torque?

Thanks for any replies.

 

[JaWiB]

First, why are you crossing the current with the magnetic field? That is, what do you expect the result of the cross product to represent?

Second, how are you crossing the current with the magnetic field considering the current goes in a circle (around the loop)?

 

[anonymousphys]

First, why are you crossing the current with the magnetic field? That is, what do you expect the result of the cross product to represent?

Second, how are you crossing the current with the magnetic field considering the current goes in a circle (around the loop)?

Don't I get the force resulting from the magnetic field when I cross the current with the magnetic field?

When I cross the current going around the loop, I am only taking the components perpendicular to the magnetic field. However, I am still getting a force that compresses the spring.

I'm still a bit confused; am I missing something?

 

[JaWiB]

>Don't I get the force resulting from the magnetic field when I cross the current with the magnetic field?

Not quite. Force on a segment of wire is $$Idl{\times}B$$ so you need to multiply by the length of the wire segment or integrate (but since you're not looking for the magnitude of the force it doesn't matter here)

I may be visualizing the situation differently than you are. Is the magnetic field always perpendicular to the current? (For instance, is the current in the x-y plane while the magnetic field is in the z direction?)

The way I picture it, both the current and the magnetic field lie in a plane. So if the current at a certain point on the loop is in the x-direction and the magnetic field is in the y-direction, then the force is in the z-direction.

 

[anonymousphys]

>
The way I picture it, both the current and the magnetic field lie in a plane. So if the current at a certain point on the loop is in the x-direction and the magnetic field is in the y-direction, then the force is in the z-direction.

Thanks for all the help so far.

I am also picturing the current and magnetic field lying in the x and y plane; just like your diagram, each loop of the coil is in an x and y plane with a different z-value. But, won't this result in a compression of the coil not torque?

The coil is similar to one take from a galvanometer.

 

[JaWiB]

Let's say the current at the bottom of one loop is going in the +x direction, while the magnetic field is in the +y direction and uniform. Using the right hand rule, at the bottom of the loop the direction of the force is in the +z direction. At the top of the loop, the current is going in the -x direction, so the force is in the -z direction.

So essentially you have a couple on the loop which gives you a net torque but no net force.

 

[anonymousphys]

Thanks for the help, I get your explanation but...
isn't the the spring just getting compressed? how do two forces create a torque about the spring?

 

[JaWiB]

No. If you were to draw a picture looking down on the coil, there is a force out of the page at the top and into the page at the bottom.

Here's a picture a google search turned up: http://www.oberlin.edu/physics/catalog/demonstrations/em/currentloop.gif

The difference is if the magnetic field is parallel to the loop, the forces pointing outward won't exist.