If you take a single coil, or loop, of wire, the magnetic fields due to every atom on the wire will add up in the center of the coil.

The magnetic field's strength can be found from:

The b-field inside of the coil of wire is either pointing into the page or our of the page. Ampere's Law, (the closed right hand rule,) is used to determine the b-field's direction. To determine the b-fields direction, "grab the imaginary loop of wire with your right while making your your thumb points in the current's direction.

The fingers show the direction of the b-field. In this case the fingers are pointing into the screen on the INSIDE of the loop. Therefore the b-field due to the current pictured here is pointing into the screen.

A solenoid is a coil of wire made up of several single loops of wire. The wire used to make a solenoid is insulated. Here is a picture of an air core solenoid that is outstretched. (From wikipedia.)

The coil is described by a couple of properties:

• the number of coils, N, counting number,
• the length of the coil, L, measured in meters [ m ],
• the permativity of the "stuff" inside the loops of wire, μ, measured in Tesla's [ T•m²/A ],
• the current pushed through it, I, measured in amps [ A ],
• and the magnetic field it generates, B, measured in Tesla's [ T ].

Below is a picture of a iron core solenoid. It would generate a stronger b-field than the aircore solenoid because it's magnetic permeability is higher.

Iron has a magnetic permeability of 0.25 T•m²/A. Compare this to air's which is nearly the same as a vacuum's at 4π x 10^-7 T•m²/A. Iron core solenoids can generate a magnetic field nearly one million times greater than an air core solenoid.

The video below describes the motion of a charged particle as it passes through a magnetic field.

Some key points to remember.

• Whenever a force is perpendicular to the velocity you get curved motion. When the force is constant, you get uniform circular motion.
• The "open right hand" rule is used to determine the direction of the moving particle.
• The force is the centripetal force for curved motion.
• "m" particel mass in [kg]
• "v" particle velocity [m/s]
• "R" radius of the curve (part of a circle) [m]saf
• "q" particle's charge [C:Coulombs]
• "B" Magnetic firld the particel is moving across [T:Tesla

• The energy/kinetic energy can be calculated easily enough from the equation for the curved motion. You can use the relationships to calculate v² and then multiply it by half the mass.
• The change in kinetic energy comes from the work that is done as the charge moves in a circle. But, since the force is perpendicular to the displacement in circular motion, work is never done and there is no change in kinetic energy.



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