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Magnetic Moments

When you place a loop of wire carrying a current in a magnetic field,
the sections of the wire that arent parallel to the magnetic 
field will experience a force
Remember,
Since there will be two sides of the loop that experience opposite
forces, a torque is exerted on the loop!

Magnetic Moments

The current flows upward in the left arm of the loop. The force exerted
by the magnetic field is into the  page.

The current  flows downward in the right side of the loop. 
The force is out  of the page.

The  combination is a torque which will rotate  the loop.

Magnetic Moments

The same situation looking from above the loop.  The current
is upward in the left wire and downward in the right wire.  The
resulting forces are shown.  Clearly, the loop experiences a torque
which will make the loop rotate.

Magnetic Moments

As the coil rotates, notice that the  effective moment arm is
decreased. This lowers the torque, although the forces are unchanged.

Magnetic Moments

Magnetic Moments

If we have N turns  of wire in
the loop


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with the magnetic field, we just throw in a sine term

Magnetic Moments

The term NIA is called the magnetic dipole moment of the coil and is actually
a vector


The direction of the area is perpendicular to the plane of the coil
These ideas are independent of the shape of the coil and depend only
on the area!

Galvanometers

We can use the applied torque to measure the current!!!
The torque is proportional to the current
Recall Hookes Law for springs

Galvanometers

The higher the current, the more we twist the spring and the 
stronger the resistive torque becomes. The rotation stops when the two
torques are equal.

We can calibrate the pointer  position with the current in the 
coil, and thus have an instrument to measure current.

Galvanometers

You may have figured out that as the coil turns, the angle changes
and the sine term comes into play.
To fix this we change the coil in a shrewd  way to take angle
out of the picture!!!

Galvanometers

We curve the poles  of the magnet and wrap the coil around an
iron core.

The iron concentrates the field lines and the curve keeps the lines
parallel to the face of  the coil!!

This takes angle out of the game.

DC Motors

Again, we need to be sneaky.   When the coil rotates to
the