Magnetic Field from a Loop

For an arc of current we derived the expression for the magnetic field at the center of the arc:

B = mo Iq / 4pR

If the arc is an entire circle, with q = 2p, we get for the field at the center:

B = mo I / 2R

The direction of the field is given by another right-hand rule. Curl the fingers on your right hand the way the current goes. Stick your thumb out and it points in the direction of the magnetic field inside the loop.

The field from a current loop looks like the field from a bar magnet (although a rather small one), which is not a coincidence. If you bring two current-carrying loops close together they will attract or repel one another, juust as bar magnets do.

Magnetic Field from Two Loops

A set of Helmholtz coils consists of two identical multi-turn coils placed close to one another. The current in each coil is the same, giving rise to a fairly uniform magnetic field in the gap between the coils. This field really looks like the field from a bar magnet.

This arrangement of coils is what you'll use in the lab this week to produce a uniform magnetic field.