Magnetism and Electromagnetic Induction

Chapters 21 and 22 of the Book

Magnets• A magnet has a north pole and a south pole.• Similar to electric charges, like poles repel and

opposite poles attract.• Poles cannot be isolated. If you cut a magnet into

two pieces, each piece will have a north and south pole.

• Magnetism is caused by the “spinning” of electrons.

Magnetic Domains• In most materials, electrons pair up with spins opposite to

each other, resulting in no net magnetism. The magnetic fields produced by ferromagnetic materials do not cancel out completely.

• In these materials large groups of atoms form with aligned spins. These groups are magnetic domains.

• When these domains experience an external magnetic field they can line up in the same orientation to enhance the overall magnetic field strength.

Permanent Magnets• Similar to charging, one magnetic object can make

another ferromagnetic material a magnet.• In a magnetically hard material, domains will

remain aligned after the first magnet is removed resulting in the creation of a permanent magnet.

• In a magnetically soft material, domains become dissociated easily.

• Domains can also become unaligned by heating or hammering.

Magnetic Field Lines• When we draw magnetic field lines, they leave the

north pole and enter the south pole. • They do not have a beginning or ending. They form

continuous loops. • Arrows on lines will indicate a field line in the plane

of the paper. Crosses show that the field is directed into the page. Circles show that the field is directed out of the page.

Magnetic Flux• Magnetic flux is a quantity that refers to the

amount of field lines that cross a given area at right angles.

Φm = ABcosƟ

• Where around a magnet is the flux greatest?

• Due to convection currents in Earth’s liquid core, Earth acts like a giant magnet.

• The Earth’s magnetic poles switch on average about every 300,000 years.

• The magnetic field shields Earth from solar wind.

Magnetism from Electricity

• In 1820, Hans Christian Oersted demonstrated that a current-carrying wire caused compass needles to be deflected.

• An induced magnetic field was created in directions tangent to concentric circles around the wire.

The Right Hand Rule• Which way is the magnetic field pointing?

1. Hold your hand as if grasping the wire.2. Point your thumb in the direction of the

current.3. The magnetic field is in the direction that

your remaining four fingers point.• The right hand rule can also be applied to a loop of

wire.

Solenoids• A solenoid combines loops of wire to increase

magnetic field strength. The greater the number of loops, the greater the field strength.

• The field of a solenoid can be increased further by inserting a ferromagnetic rod in the center. This is called an electromagnet.

Magnetic Force• When a charge moves through a constant magnetic

field, it experiences a force.F=qvB

(for a charge moving perpendicular to the field)• The unit of a magnetic field is the Tesla (T). 1 T is equal

to the field strength that would act on 1 C of charge moving at 1 m/s with a force of 1 N.

• A Tesla is a large quantity. The magnetic field of the Earth is ~ 50 µT. The LHC superconducting magnets can generate a 30 T field.

Another Right Hand Rule• Which way does the force push the charge?

1. Put your fingers along the direction of the field.

2. Point your thumb in the direction of the charge’s velocity.

3. Your palm will point in the direction of the magnetic force.

Particle in a Magnetic FieldA proton moving east experiences a force of 8.8x10-19

N upward due to the Earth’s magnetic field. At this location, the field has a magnitude of 5.5x10-5 T to the north. Find the veloctiy of the particle.

Magnetic Force on Wires• The force experienced by a current-carrying wire is

the sum of all of the individual forces of the electrons moving within it.

F = BIlThe parallel wires near each other will experience magnetic force: towards each other if the current is

in the same direction and away if it is in opposite directions.

• A speaker uses the force on a coil of wire to vibrate a cone that transmits sound.

Electromagnetic Induction• Just as a flow of current can generate a magnetic field,

a change in the flux of a magnetic field can create a flow of current.

• As long as there is relative motion between a magnet and a wire, there will be an induced current.

• The magnetic force pushes charges in along the wire similar to the electric force created by a battery.

• The angle of the wire affects the current. It is maximized if the wire is perpendicular to the field, zero if the wire is parallel.

3 Ways of Inducing a Current

1. A circuit is moved into or out of a magnetic field.

2. A circuit is rotated in a magnetic field.3. The intensity or direction of a magnetic field

is varied.

Induced Current Continued• Consider a bar magnet approaching a coil of wire.• As the magnet approaching the coil, the magnetic

field passing through the coil increases in strength. The increasing induced current generates an increasing magnetic field that opposes that of the bar magnet.

• The opposite situation occurs as the bar magnet is moved away from the coil. However, the magnetic field still opposes the movement of the magnet.

Lenz’s Law.• This is Lenz’s Law.• The magnetic field in an induced current is in a

direction that opposes the change that caused it.

Faraday’s Law of Induction• Michael Faraday calculated the magnitude of

electromotive force (emf) caused by induced current.

emf = -NΔφm/Δt

• emf is measured in volts. N is the number of loops in a wire. What factors go into flux?

Induced emfA coil with 25 turns of wire is wrapped around a

hollow tube with an area of 1.8 m2. Each turn has the same area as the tube. A uniform magnetic field is applied at a right angle to the plane of the coil. If the field increases uniformly from 0.00 T to 0.55 T in 0.85 s, find the magnitude of the induced emf in the coil. If the resistance in the coil is 2.5 Ω, find the magnitude of the induced current.

Electric Guitars• Electric guitars use a device called a pickup to

change mechanical energy into electrical energy.• A pickup consists of a permanent magnet wrapped

in a copper wire. The number of wrappings determine the current that the pickup produces.

• Guitar strings are slightly magnetic. When one is plucked it changes the magnetic field above the pickup, resulting in a change in the magnetic field and therefore a current.

Generators• A more practical way of generating electricity is to

move the wire, not the magnet.• A generator uses mechanical energy to move a coil

of wire in a magnetic field inducing a current in the wire.

• Generators produce alternating currents, but ac can be changed to dc.

Motors• A motor converts electrical energy to mechanical

energy. In essence, this is a generator in reverse.• Keep in mind that as the coil of wire turns through

the magnetic field, it induces an emf that opposes the current already in the wire. This is called back emf.

• The back emf will become larger as the motor turns faster.

Transformers• A transformer uses an alternating current in one

coil of wire to induce an alternating current in another coil of wire.

• The voltage of the induced current can be affected by changing the number of loops.

Transformer EquationV2 = V1 (N2/N1)

• N1 is the primary coil. N2 is the secondary coil.

• A step-up transformer is used on a 120 V line to provide a potential difference of 2400 V. If the primary has 75 turns, how many turns must the secondary have?