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