A permanent magnet has a north magnetic pole and a south magnetic pole. Like poles repel; unlike poles attract.

A magnetic field surrounds a magnet. The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point.

Magnetic field lines can be used to show the magnetic field in the same way that we used electric field lines in an earlier chapter.

The magnetic field is stronger where the field lines are closer together. This is true near the poles of a magnet.

Between the poles of a horseshoe magnet the magnetic field lines are nearly parallel and equally spaced, there the magnetic field is approximately constant.

The direction of a magnetic field is indicated by arrows if it is parallel with the surface of the page. A field directed perpendicularly out of a page is indicated by spots. A field directed perpendicularly into a page is indicated by X’s.

Field directed out of page Field directed into page

A charge placed in a magnetic field experiences magnetic force

if two conditions are met:1) The charge must be moving; no magnetic force acts on a stationary charge. 2) The velocity must have a component that is perpendicular to the magnetic field.

Right-Hand Rule #1: If the fingers point along the magnetic field and the thumb indicates the direction of the velocity of the positive charge, the palm faces in the direction of the magnetic force.

The magnitude B of the magnetic field at any point in space:

B = F/q0v(F = qvB) The unit is the newton•second/coulomb•meter which is equal to 1 tesla (T)

A coulomb/second =

1 ampere, so 1 T = 1 N/(A•m)

1 gauss = 10-4 tesla

Ex. 1 - A proton in a particle accelerator has a speed of 5.0 x 106 m/s. The proton encounters a magnetic field whose magnitude is 0.40 T. Find (a) the magnitude and direction of the magnetic force on the proton, (b) the acceleration of the proton. (c) What would be the force and acceleration if the particle were an electron instead of a proton?

In an electric field, a moving positive charge is deflected in the direction of the field lines. In a magnetic field, a moving positive charge is deflected at right angles to the direction of the magnetic field lines.

Since the magnetic force is always at right angles to the motion of a particle in a magnetic field, The magnetic force cannot do work and change the kinetic energy of the particle (as an electric field can).

The magnetic force is always perpendicular to the velocity and is directed toward the center of the circular path (a centripetal force).

Remember, FC = mv2/r and FC = qvB,

so qvB = mv2/r or r = mv/qB

Example 2: A proton enters a region of constant magnetic field of 0.20 T. The velocity is6 x 105 m/s and the direction is 90° to the direction of the field. Find the radius r of the circular path on which the proton moves in the magnetic field.

Ex. 3 - A proton is released from rest at point A, next to the positive plate of a parallel plate capacitor. The proton accelerates toward the negative plate, exiting the capacitor through an opening. The potential of the positive plate is 2100 V greater than that of the negative plate. Once outside the capacitor, the proton enters a region of constant magnetic field of 0.10 T. The field is directed out of the board. Find (a) the speed vB of the proton when it leaves the negative plate, and (b) the radius r of the circular path on which the proton moves in the magnetic field.

A charge moving in a magnetic field can experience a magnetic force. A current in a magnetic field can also experience a magnetic force. The direction of the positive charge is replaced by the conventional current I.

The force on a charge is F = qvB. Current is ∆q/∆t. F = qvB times ∆t/∆t becomes, F = (∆q/∆t)•v∆t B. ∆q/∆t = I, and v∆t = length, so F = ILB.

The magnetic force on a current-carrying wire of length L (when the angle of the wire loop to the magnetic field is 90º), is given by:

F = ILB

The force is maximum when the current carrying wire is oriented perpendicular to the field, it is zero when the current moves parallel or antiparallel to the field.

Example 4: A 2 m length of wire is placed perpendicular to a 0.10 T magnetic field. The current in the wire is 4 A. Find the magnetic force that acts on the length of wire.

The direction of the magnetic force is given by RHR-1.Magnetic force is used to produce sound in a loudspeaker.

Ex. 5 - The voice coil of a speaker has a diameter of d = 0.025 m, contains 55 turns of wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is 2.0 A. (a) Determine the magnetic force that acts on the coil and cone. (b) If the voice coil and cone have a combined mass of 0.020 kg, find their acceleration.