1. Review and some interesting consequences of F=qvxB.
Today’s agenda:
Review and some interesting consequences of F=qvxB.
You must understand the similarities and differences between electric forces and magnetic forces on charged particles.
Magnetic forces on currents and current-carrying wires.
You must be able to calculate the magnetic force on currents.
Magnetic forces and torques on current loops.
You must be able to calculate the torque and magnetic moment for a current-carrying wire in a uniform magnetic field.
Applications: galvanometers, electric motors, rail guns.
You must be able to use your understanding of magnetic forces and magnetic fields to describe how electromagnetic devices operate.

2. Magnetic Forces on Currents
So far, I’ve lectured about magnetic forces on moving charged particles.
Actually, magnetic forces were observed on current-carrying wires long before we discovered what the fundamental charged particles are.
Experiment, followed by theoretical understanding, gives
For reading clarity, I’ll use L instead of the l your text uses.
If you know about charged particles, you can derive this from the equation for the force on a moving charged particle. It is valid for a straight wire in a uniform magnetic field.

3. Here is a picture to help you visualize
Here is a picture to help you visualize. It came from
Homework Hint
For fixed L, B: this is the biggest force you can get from a given current I.
For bigger F, you need bigger I.

4. Valid for straight wire, length L inside region of magnetic field,                 I B L                
Valid for straight wire, length L inside region of magnetic field,
constant magnetic field, constant current I, direction of L is direction of conventional current I.
You could apply this equation to a beam of charged particles moving through space, even if the charged particles are not confined to a wire.

5. What if the wire is not straight?                     B        ds        dF       
Integrate over the part of the wire that is in the magnetic field region.
Homework Hint: if you have a tiny piece of a wire, just calculate dF; no need to integrate.

6. Note: I generally use ds for an infinitesimal piece of wire, instead of dl.
Font choice may make “l” look like “1.”
It’s a pain to search the fonts for a script lowercase l: l.