Magnetic Fields and Magnetic Forces

Magnetic Fields arise from current flows. In the drawing below, a Solenoid is shown:

A Solenoid is a wire connected to the poles of a battery (source of voltage not shown in the picture) that has been coiled as shown above. The flow of current through the coil produces a magnetic field. To see how this works, consider the simpler case of one wire:

The current flows upward producing a magnetic field whose field lines wind circularly about the current flow. The direction in which the field circles is given by the right hand rule. As viewed from the North (top), the field circles in the counterclockwise sense. Magnetic fields obey the Principle of Superposition. So whenever we have two fields, the field where they occupy the same space is simply the sum of the two individual fields. In this way, we may study very complicated field configurations by adding up the contributions from each part of the system.

Q: How do currents interact with each other (through their magnetic fields)?

The interaction is described by the Lorentz Force which has the consequence of

The way this works is a little tricky, but let's think about it. Wire 1, produces a magnetic field at the location of wire 2. This magnetic field, B interacts with the current to produce a force.

Wire 1 produces a field that circles around the wire as shown. The charged particles then feel a force as they move through the field. The direction of the force is shown on the above figure.

• The current flows upward in wire 2 and the field B at the wire is into the paper. The force is perpendicular in direction to both the current and B
• The direction is found by laying the back of your right hand in the direction the current flows with the orientation such that your fingers curl toward the direction of the magnetic field B.
• In this configuration, your extended thumb points in the direction of the force (the Lorentz Force). (For the mathematically inclined, the direction of the force is given by the curl of I and B, I X B.)

This has the consequence that for currents which flow in the same direction, the magnetic force pulls the wires together. Q: Do currents always attract, is this true in general? No, parallel currents (same direction) attract each other while anti-parallel currents (oppositely directed currents) repel each other.

This has the consequence that when a current (particle beam) moves through a magnetic field, it is deflected:

In a less obvious way, this also says that magnets when placed in the vicinity of other magnets force each to align as: