The force on a current-carrying wireA magnetic field exerts a force on a single moving charge, so it's not surprising that it exerts a force on a current-carrying wire, seeing as a current is a set of moving charges.

Using q = I t, this becomes:

But a velocity multiplied by a time is a length L, so this can be written:

The direction of the force is given by the right-hand rule, where your fingers point in the direction of the current. Current is defined to be the direction of flow of positive charges, so your right hand always gives the correct direction.

sinF qvB sinF IvtB

sinF ILB

Three wires

Consider three wires carrying identical currents between two points, a and b.

The wires are exposed to a uniform magnetic field.

Wire 1 goes directly from a to b. Wire 2 consists of two straight sections, one parallel to the magnetic field and one perpendicular to the field. Wire 3 takes a meandering path from a to b. Which wire experiences more force?

1. Wire 1

2. Wire 2

3. Wire 3

4. equal for all three

Three wiresThe force is equal for all three. What matters is the displacement perpendicular to the field, and that's equal for all wires carrying equal currents between the same two points in a uniform magnetic field.

The force on a current-carrying loop

A wire loop carries a clockwise current in a uniform magnetic field directed into the page. In what direction is the net force on the loop?

1. Left

2. Right

3. Up

4. Down

5. Into the page

6. Out of the page

7. The net force is zero

The force on a current-carrying loop

The net force is always zero on a current-carrying loop in a

UNIFORM magnetic field.

Is there a net anything on the loop?

Let’s change the direction of the uniform magnetic field. Is the net force on the loop still zero? Is there a net anything on the loop?

Is there a net anything on the loop?

Let’s change the direction of the uniform magnetic field. Is the net force on the loop still zero? Is there a net anything on the loop?

The net force is still zero, but there is a net torque that tends to make the loop spin.

The torque on a current loopThe magnetic field is in the plane of the loop and parallel to two sides. If the loop has a width a, a height b, and a current I, then the force on each of the left and right sides is F = IbB. The other sides experience no force because the field is parallel to the current in those sides. Simulation

The torque ( ) about an axis running through the center of the loop is:

sinrF

2 2

a aF F

aF

IabB

The torque on a current loop

ab is the area of the loop, so the torque here is .

This is the maximum possible torque, when the field is in the plane of the loop. When the field is perpendicular to the loop the torque is zero. In general, the torque is given by:

IabB IAB

sinIAB

where is the angle between the area vector, A, (which is perpendicular to the plane of the loop) and the magnetic field, B.

A DC motorA direct current (DC) motor is one application of the torque exerted on a current loop by a magnetic field. The motor converts electrical energy into mechanical energy.

If the current always went the same way around the loop, the torque would be clockwise for half a revolution and counter-clockwise during the other half. To keep the torque (and the rotation) going the same way, a DC motor usually has a "split-ring commutator" that reverses the current every half rotation. Simulation

The force between two wires

A long-straight wire carries current out of the page. A second wire, to the right of the first, carries current into the page. In which direction is the force that the second wire feels because of the first wire?

1. Left

2. Right

3. Up

4. Down

5. Into the page

6. Out of the page

7. The net force is zero

The force between two wiresIn this situation, opposites repel and likes attract!

Parallel currents going the same direction attract.

If they are in opposite directions they repel.

A loop and a wire

A loop with a clockwise current is placed below a long straight wire carrying a current to the right. In which direction is the net force exerted by the wire on the loop?

1. Left

2. Right

3. Up

4. Down

5. Into the page

6. Out of the page

7. The net force is zero

A loop and a wire

The long straight wire creates a non-uniform magnetic field, pictured below.

A loop and a wire

The forces on the left and right sides cancel, but the forces on the top and bottom only partly cancel – the net force is directed up, toward the long straight wire.

The field from a solenoidA solenoid is simply a coil of wire with a current going through it. It's basically a bunch of loops stacked up. Inside the coil, the field is very uniform (not to mention essentially identical to the field from a bar magnet).

For a solenoid of length L, current I, and total number of turns N, the magnetic field inside the solenoid is given by:

0NIBL

The field from a solenoid

We can make this simpler by using n = N/L as the number of turns per unit length, to get: .

The magnetic field is almost uniform - the solenoid is the magnetic equivalent of the parallel-plate capacitor. If we put a piece of ferromagnetic material (like iron or steel) inside the solenoid, we can magnify the magnetic field by a large factor (like 1000 or so).

0NIBL

0B nI

Magnetism on the atomic level

Currents in wires produce magnetic fields. What produces the magnetic field from a bar magnet, where there are no wires? Why does that field look like the field of a solenoid?

Consider the Bohr model of the atom, where electrons travel in circular orbits around the nucleus. An electron in a circular orbit looks like a current loop, so it produces a magnetic field. In some materials (ferromagnetic materials) the magnetic moments associated with the atoms align, leading to a large net magnetic field.

Whiteboard