Creating Magnetic Fields

Text: Ch. 20 M. Blachly, AP Physics

Magnetic Field

Magnetic fields are created by moving charges.

For a long, straight wire, the magnetic field circulates around the wire.

Magnetic Field

Direction of B is given by right hand rule: Thumb in direction of current, fingers curl in the direction of B

Ampère’s Law

Ampère’s law relates the magnetic field around a closed loop to the total current flowing through the loop.

0 encB dl I

Ampère’s law can be used to calculate the magnetic field in situations with a high degree of symmetry.

Ampère’s Law

Magnetic Field of a Long Straight Wire

The field is inversely proportional to the distance from the wire:

The constant μ0 is called the permeability of free space, and has the value:

Summary

A current moving in a wire produces a magnetic field

A magnetic field produces a force on a wire that carries a current.

Two Wires

What will happen if there are two long, parallel wires that each carry a current?

I1

I2

d

Force between Two Parallel Wires

The magnetic field produced at the position of wire 2 due to the current in wire 1 is:

The force this field exerts on a length l2 of wire 2 is:

Force between Two Parallel Wires

Parallel currents attract; antiparallel currents repel.

A loop of wire

What if we bend our wire into a loop?

Solenoid

What if we bend our wire into lots of loops?

oB nI

The Right-hand Rule

Magnetic Materials

Electrons “orbit” the nucleus and also “spin”. This produces a magnetic field

Electrons generally pair up

• most of the magnetic field cancels

Magnetic Materials

In some materials, the magnetic fields do not cancel

iron, cobalt and nickel

The atoms “align” in a small region and create a domain.

The domains persist when the external magnetic field is removed

Also called “hard” magnets or permanent

Paramagnetic material

The magnetic spins align in small regions forming a domain.

Domains can align with an external magnetic field

The domains do not persist when the external magnetic field is removed

Also called “soft” magnets

Nonmagnetic material

Atom has no net magnetic moment so there can be no domain

Exhibits no magnetic effects: magnets cannot “stick” to nonmagnetic metals

Example: copper, stainless steel

Cores

Adding a core to a solenoid can greatly increase the magnetic field strength.

Applications

A galvanometer takes advantage of the torque on a current loop to measure current.

An electric motor also takes advantage of the torque on a current loop, to change electrical energy to mechanical energy.

Applications

Loudspeakers use the principle that a magnet exerts a force on a current-carrying wire to convert electrical signals into mechanical vibrations, producing sound.

Applications

A mass spectrometer measures the masses of atoms. If a charged particle is moving through perpendicular electric and magnetic fields, there is a particular speed at which it will not be deflected:

Applications

Mass Spectrometer

All the atoms reaching the second magnetic field will have the same speed; their radius of curvature will depend on their mass.

Links

Additional Links:

http://www.physics.sjsu.edu/becker/physics51/induction.htm

http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/magcon.html#c1

All about how audio speakers work: http://electronics.howstuffworks.com/speaker6.htm