Magnetic Forces and Magnetic Fields

Chapter 21

21.1 Magnetic Fields

Magnets, as you know, can exert forces on one another.

In electricity, we talk about negative and positive dipoles or charges.

In magnetism, we discuss north and south poles.

Like poles repel each other, and unlike poles attract.

Electric charges vs. Magnets

ELECTRIC CHARGES

Can be positive or negative

Positive and negative charges can be separated so that a (+) or (-) charge is isolated.

Produce an electric field that is a vector quantity

Electric field points away from positive and toward negative

MAGNETS

Have a negative end and a positive end.

ALL MAGNETS have a negative and positive or north and south end.

Produce a magnetic field that is a vector quantity

Magnetic field direction is determined by the direction of the north pole of a compass at a particular point

Lines tend to originate at north and end at south without stopping in between

Some Vocabulary

Angle of declination: angle that a compass needle deviates from the north geographic pole

Angle of dip: the angle that the magnetic field makes with respect to the surface at any point

Magnetic north pole: true north pole as generated by the earth due, most likely, to currents of iron moving in the core

Geographic north pole: where the Earth’s axis of rotation crosses the surface in the Northern Hemisphere

Click here for an interactive description of the difference.

21.2 The Force that a Magnetic Field Exerts on a Moving Charge

Magnetic force can be added to our bucket list of forces that can cause objects to accelerate and can be used in conjunction with Newton’s 2nd Law of Motion.

For a Charge to Experience a magnetic force when place in a field:

1. The charge must be moving, for no magnetic force acts on a stationary charge.

2. The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field.

Force on Moving Charge

If the charge moves parallel or antiparallel to the field, the charge experiences no magentic force.

If the charge moves perpendicular to the field, the charge experience the maximum possible magnetic force.

If the charge moves at an angle, θ, only the velocity component (vsinθ), perpendicular to the field gives rise to a magnetic force.

Right-Hand Rule #1

Extend the right hand so the fingers point along the direction of the magnetic field (B) and the thumb points along the velocity of the charge. The palm of the hand, then, faces in the direction of the magnetic force that acts on a positive test charge.

If the moving charge is negative, the direction of the magnetic force is opposite from described above.

Definition of Magnetic Field

sin

FB

0 vq

• Direction of field is determined by a small compass needle.• SI Unit: Newton second/coulomb meter = 1 Tesla• If magnetic field is much less than one Tesla, a gauss (G) is often used as a unit for magnetic field.• 1 gauss = 10-4 tesla

21.3 Motion of a Charged Particle

ELECTRIC FIELD

Direction of electric force is same as direction of electric field

Force does work and increases KE

MAGNETIC FIELD

Direction of magnetic force is always perpendicular to magnetic field and velocity

Since displacement and force are perpendicular, no work is done by this force

Force changes direction but not magnitude of velocity

The Circular Trajectory

When a +q charge is moving perpendicular to a magnetic field, the magnetic force causes the particle to move in a circular path.

Radius of the circle is inversely proportional to the magnitude of the magnetic field

Stronger fields produce “tighter” circular paths

The Force on a Current in a Magnetic Field

Since an electric current is a collection of moving charges, a current in the presence of a magnetic field can also experience a magnetic force

Modify RHR-1 by replacing direction of velocity with direction of conventional current in order to determine direction of force.

The magnetic force is maximum when the wire is oriented perpendicular to the magnetic field.

Magnetic Force on current-carrying wire

Simplified, this equation becomes

The direction of the force of the magnetic field is determined by using RHR-1 as explained on previous slide.

If the direction of the current changes, the direction of the force will also change.

The Torque on a Current-Carrying Coil

If a loop of wire is suspended properly in a magnetic field, the magnetic force produces a torque that can rotate the loop.

This torque is responsible for the operation of an electric motor.

When a current-carrying loop is placed in a magnetic field, the loop tends to rotate such that its normal becomes aligned with the magnetic field.

Basically, the current loop behaves like a magnet suspended in a magnetic field.

Physics of DC Electric Motor http://

hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motdc.html#c1

http://www.learnapphysics.com/apphysicsb/magnetism.php

Magnetic Fields Produced by Currents

A current-carrying wire will produce a magnetic field of its own.

A compass needle will align itself with the net magnetic field produced by a current and the magnetic field of the earth

Thus, the beginning of the study of electromagnetism.

Long, Straight Wires

Compass needles indicate that the magnetic field lines produced by the current are circles centered on the wire.

If the current reverses, the needles reverse.

Direction of field found by RHR-2 RHR-2: curl the fingers of the right hand

into the shape of a half circle. Point the thumb in the direction of the conventional current, I and the tips of the fingers will point in the direction of the magnetic field

Long, Straight Wires

Magnitude of B is directly proportional to I and inversely proportional to the radial distance from the wire

is known as the permeability of free space with a value of 4π x 10-7 Tm/A