Study Guide

# Electricity and Magnetism - Magnetic Forces

## Magnetic Forces

Of course, fields are great and all—but it's a field's ability to do work that makes them interesting. Magneto would be a way less interesting supervillain if magnetic fields couldn't create forces ("Behold! I'm creating invisible things that do nothing! Quiver in fear, mortal men!").

Gravity. Electric fields. They both have strong forces associated with them, and—fortunately for physics but less so for the X-Men—so too does the magnetic field. However, just like gravity only works on things with mass, and electric fields only work on things with charge, magnetic fields only work on other magnets. Remember, though, that a magnet doesn't have to be a big, red and white horseshoe. Any moving charge or current creates a magnetic field, and is therefore subject to magnetic forces.

The magnetic force is defined by the Lorentz force law. The Lorentz force is the force felt by a charge q moving with speed v in a magnetic field B, and is given by:

Fb = qvBsinθ

θ is the angle between the charge's trajectory and the direction of the magnetic field lines. A charge moving perpendicular to a magnetic field will feel its full force (sin 90º = 1), but a charge traveling parallel to a field won't feel anything at all (sin 0º = 0).

We can extend this to current-carrying wires, as well. A wire of length l in a magnetic field B will feel a force dependent on the amount of current (that is, moving charge) in the wire:

Fb = lIBsin θ

Fb points in a direction determined by right hand rule #2. Point your index finger in the direction the charge is moving (either in the direction of v or I), point your middle finger in the direction of B, and give a thumbs up. Your thumb is now pointing in the direction of Fb, and Siskel and Ebert would be proud.

When we combine the Lorentz force with the Coulomb force, we now have a full description of the electromagnetic forces on a charged particle:

F = Fe + Fb = qE + qvBsinθ

### Common Mistakes

The right hand rule can be... unruly. Remember Index finger is for current (I for an I), Middle finger is for Magnetic field, and your thumb is the result.

### Brain Snack

Lest you think the magnetic force pales in comparison to other forces we've talked about, we present the U.S. Navy's research into magnetic cannons called railguns.

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