Magnetism

Magnetic materials have the ability to attract or repel other types of magnetic materials.

But not all materials are magnetic

The origin of magnetism is moving electrical charge. Electrons move around the nucleus in electrons clouds, but they also spin around their own axis.

These atoms cluster together to form magnetic domains.

Having domains only gives a material the ability to become a magnet.

Atoms of non-magnetic materials have a balance of electrons that spin clockwise and counterclockwise.

Atoms of magnetic materials have an imbalance of spinning electrons – more electrons spinning one way versus the other.

In order for a material with domains to become magnetic, the domains have to be aligned by an external magnetic field.

If enough of a materials domains become aligned, the material forms a magnetic dipole and becomes a permanent magnet.

A magnetic dipole is made up of two poles – a north pole and a south pole.

Poles cannot be isolated – a magnet cannot be broken to get a separate north and south pole. Instead, it creates two magnets, each with a north and south pole.

Rules of Interaction

Like poles repel

Opposite poles attract

Magnets can exert forces on each other without making contact, proving that there are magnetic fields that surround them.

Magnetic field lines always project externally out of the north pole of a magnet and are directed into a south pole.

The field is stronger in areas where the field lines are closer together.

Other magnets align themselves along the tangents of a magnet’s field lines

Magnetic and Electric Fields Interactions

When a current-carrying wire is placed in a magnetic field the magnetic field exerts a force on the wire.

Assuming the wire is perpendicular to the field lines, the force is always perpendicular to both (utilizing x, y, and z axes)

To determine the direction that the force exerts on the wire, use the right-hand rule.

Thumb points in direction of electric current

(flows + to -)

Fingers point in direction of magnetic field lines

(project from N to S)

Palm points in direction of force

When something is perpendicular to paper, use following symbols

-- into paper -- out of paper

First…find your RIGHT hand

The magnitude of the force is determined by the amount of current in the wire, the length of the wire in the field, and the strength of the magnetic field/

F = BIlsinθF = force (N)

B = magnetic field (Tesla)

I = current (A)

l = length of wire in field (m)

θ = angle between field lines and wire

The magnitude of the force is determined by the component of the current that is perpendicular to the field.

If the wire was parallel, there would be NO force on it.

A rectangular loop of wire hangs vertically in a horizontal magnetic field. The uniform magnetic field points out of the page. If the current is 0.245 A and the magnetic field is 1.42 T, what is the net force acting on the loop?

The same phenomenon shows up when a single charge moves through a magnetic field. Single positive charges obey the right hand rule

If a negative charge moves through a field, the force is in the opposite direction of the force for a positive charge.

F = qvBsinθF = force (N)

B = magnetic field (Tesla)

q = charge (C)

v = speed of particle (m/s)

θ = angle between field lines and path of charge

An electron travels at 2.0 x 107 m/s in a plane perpendicular to a uniform 0.010-T magnetic field. What is the radius of its path?

This spiral path is what is responsible for the aurora borealis at the Earth’s poles.

Charged particles from the solar wind interact with the magnetic field of the Earth which forces their trajectory into a circular motion.

We know that when current is placed in a magnetic field, the magnetic field exerts a force on the wire.

A wire also has its own magnetic field that can apply a force on objects that are placed in the field.

Thumb points in direction of electric current

(flows + to -)

Fingers curl in direction of magnetic field lines

Right-hand Rule #2

There is NO external magnet present. Magnetic field caused by moving charge in wire.

B = μ0I/2πrB = magnetic field (T)

I = current (A)

μ0 = permeability constant (4π x 10-7 Tm/A)

r = distance to wire

To find the magnitude of the magnetic field, use the following formula:

A magnetic field is a vector product like an electric field – direction maters.

Two parallel wires 10.0 cm apart carry currents in opposite directions. Current I1 = 5.0 A is out of the page and I2 = 7.0 A is into the page. What is the magnitude and direction of the magnetic field halfway between the two wires.

Electromagnetic Induction

We have observed how a current-carrying wire in a magnetic field produces a force on the wire.

Can the opposite be true? Can a moving magnetic field around a wire produce a current?

This phenomenon is called electromagnetic induction.

In the 1830’s, Michael Faraday created an apparatus in which an insulated wire is wrapped around a ring. The ring was also attached to a galvanometer, which measures very small current.

Faraday noticed that a constant current did not produce a current in the galvanometer. But at the instant he turned it on or off, the needle moved.

It wasn’t a constant current that induced another current. It was a changing current.

English chemist and physicist

1791 - 1867

Furthermore, what was important was not the changing current, but the changing magnetic field in the ring.

As the current was increasing, it was increasing the magnetic flux in the ring

Magnetic flux –the number of magnetic field lines that passes through a given area

Magnetic Flux

ФB = BAcosθФB = magnetic flux (Weber)

B = magnetic field (T)

A = area bound by wire (m2)

θ = angle between magnetic field lines and perpendicular to plane of area

The only part of the magnetic field that contributes to magnetic flux is the component that is perpendicular to area bound by the wire.

A square loop of wire with sides 10.0 cm long is turning in a 1.25-T magnetic field. What is the change in flux between when the loop is perpendicular to the field lines and when the loop is at a 35° angle to the field lines?

Faraday’s Law of Induction

Faraday proposed that current is produced because of a changing magnetic flux in the iron ring.

He theorized Faraday’s Law, which states that a changing magnetic flux over time creates electromotive force and subsequent induced current in the other wire.

E = - N∆ФB / ∆tN = number of loops

E = electromotive force (V)

∆ФB = change in magnetic flux (Wb)

∆t = time interval (s)

There are many ways to change the magnetic flux inducing a current. Again, if the number of field lines in the loop changes, the flux changes.

How is the flux changed in each situation?

a) the change in flux through the coil

a) the emf and current induced

A square coil of wire with 5.00-cm sides contains 100 loops and is positioned perpendicular to a uniform 0.600-T field. It is quickly pulled from field at a constant speed to a region where there is no magnetic field. If the right edge of the coil is at the edge of the field, it takes 0.100 s for the whole coil to reach the field-free region. Assuming the coil has a resistance of 100 Ω, find the following:

Lenz’ Law

E = - N∆ФB / ∆tObvious question – Why is the emf negative?

The current produced by an induced emf moves in a direction so that its magnetic field opposes the original change in flux.

This is known as Lenz’s Law.

Flux decrease current moves so magnetic field coincides

Flux increase current moves so magnetic field counteracts

A 30.0-cm conducting rod with a resistance of 2.5 Ω moves on a U-shaped conductor with a speed of 1.6 m/s. The resistance of the U-shaped conductor is 25.0 Ω and it is in a uniform magnetic field of 0.35 T.

Calculate the induced emf over a 0.5-s time interval.

Calculate the current (magnitude and direction) in the conductor.