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Magnetic Fields and Magnetic Forces

Properties of magnets:

  1. A magnet has polarity - it has a north and a south pole; you cannot isolate the north or the south pole (there is no magnetic monopole)
  2. Like poles repel; unlike poles attract
  3. A compass is a suspended magnet (its north pole is attracted to a magnetic south pole); the earth’s magnetic south pole is within 200 miles of the earth’s geographic north pole (that is why a compass points "north")
  4. Some metals can be turned in to temporary magnets by bringing them close to a magnet; magnetism is induced by aligning areas called domains within a magnetic field
  5. Permanent magnets are formed of metallic alloys or metals such as iron, nickel, or cobat

Magnetic field (symbol is B and SI unit is the Tesla or T
the environment around a magnet in which the magnetic forces act

Magnetic field lines
they represent the area around a magnet; magnetic field lines flow from north to south

Domain
Atoms of ferromagnetic materials act in groups called domains; atomic magnets in each domain are aligned so that each domain is a microscopic bar magnet; the domains align themselves with an external magnetic field

Oersted (1820) found that an electric current in a wire produces a magnetic field around it; a stationary charge does not create a magnetic field

right-hand rules predict the direction of magnetic fields produced by a current. They are used for conventional current flow. Use your left hand to predict the direction an electron or negative charge would follow.

RHR #1 - Straight Wire Conductor

Curl the fingers of the right hand into the shape of a circle. Point the thumb in the direction of the current and the tips of the fingers will point in the direction of the magnetic field.

right hand rule 1 right hand rule 1

RHR #2 - Solenoid

Curl the fingers of the right hand in the direction of the current. Your thumb is the north pole of the electromagnet.

solenoid right hand rule

RHR #3 - Magnetic Force

Extend the right hand so that the fingers point in the direction of the magnetic field and the thumb points in the direction of the current. The palm of the hand then pushes in the direction of the magnetic force.

right hand rule for forces

Forces Due to Magnetic Fields

Ampere found that a force is exerted on a current-carrying wire in a magnetic field

F = B I L sin f
where B is the magnetic field in Teslas (T), I is the curent, L is the length of wire in meters, and f is the angle. Only the perpendicular component of B exerts a force on the wire.

We know how to measure force, current, and length. Thus B can be calculated by using

magnetic field strength

The force produced by a magnetic field on a single charge depends upon the speed of the charge, the strength of the field, and the magnitude of the charge.

F = q v B sin f
where q is the charge in Coulombs and v is the velocity of the charge

The magnetic field at any point a distance R away from a straight-wire conductor can be calculated using,

magnetic field around a straight wire conductor

Electromagnetic Induction

Faraday found that a current could be induced in a wire by moving it in a magnetic field. An electric current is generated in a wire when the wire cuts across magnetic field lines.

Electromagnetic induction
process of generating a current by using a magnetic field
emf = B L v sin f
where emf is the potential difference measured in volts, v is the velocity with which the wire is moved through the magnetic field B, p is the angle at which the wire is moved in the magnetic field, and L is the length of the wire

electromotive force (emf)
a potential difference, measured in volts, that can cause an induced current to flow in a wire. It is not a force, but is a historical term coined before electricity was understood.

Electric Motors and Generators

Electromagnetic Induction
the process where current is produced when either a wire or a magnetic field move relative to one another; as long as the wire cuts across magnetic field lines during the motion, a current is produced.

Electric motor
uses electrical energy to produce mechanical energy. In a motor, there must be a source of a magnetic field; brushes serve as a connection to the split-ring commutator, allowing current flow from the motor to an outside source. In order to continue rotating, current direction must be reversed. This is achieved by the use of the split-ring commutator and the brushes. The force on a current-carrying wire in a magnetic field causes an electric motor to rotate

Electric generator
uses mechanical energy to create electrical energy; rotation of wire loop in a magnetic field causes current to be induced. This current changes direction every 180 degrees, producing alternating current (AC current).

Lenz's Law
The direction of the induced current is such that the magnetic field resulting from the induced current opposed the change in the flow (or flux) that caused the induced current. It is the change in the flow or flux that causes the induced current, not the flux itself.

Self-inductance
induced emf produced in a coil by a changing current

Mutual inductance
a changing current in one coil induces an emf in another coil

Transformer
an electrical device that increases or decreases AC voltage; a step-up transformer has more turns in the secondary than in the primary; a step-down transformer has more turns in the primary than in the secondary.

transformer equation

where N is number of turns, V is the voltage, and I is the current. s and p stand for secondary and primary, respectively.

Magnetism Sample Problems

Magnetism Homework