Electromagnetic induction question

[bill nye scienceguy!]

How do I calculate the force (in Newtons) acting on a conductor moving through a magnetic field? This is in relation to an electromagnetic brake by the way; I need to work out the deceleration of train as it moves through the braking zone.

Thanks.

 

[lpfr]

Force is $$\vec F=I\ell \vec u\times\vec B$$
Here $$\vec u$$ is a vector parallel to the current and pointing in the same direction.
$$I$$ and $$\ell$$ are the current and the conductor length.

 

[bill nye scienceguy!]

Thanks! As an aside, how would you work it out if you use a permanent magnet rather than an electromagnet?

 

[lpfr]

The origin of B doesn't matter, it can be generated by an electromagnet as well as by a permanent magnet.

 

[bill nye scienceguy!]

so the equation remains the same? does that mean there has to be a current in the conductor rather than in the magnet?

 

[lpfr]

Yes. No current, no force.
In a magnetic brake the current in induced by the varying magnetic flux.
Only electromagnets need current to generate the magnetic field.

 

[bill nye scienceguy!]

Thanks for all that, I wish I'd had this discussion 2 months ago - would have made a project much easier.