Magnetic Fields

Magnetic field = force field surrounding a magnet or current-carrying wire, which acts on any other magnet or current-carrying wire in the field

• Magnetic field of a bar magnet strongest at its poles (North-seeking and South-seeking poles)

• A line of force/magnetic field line is a line along which a north pole would move in the field - always go from North to South

Force on a Current-Carrying Wire in a Magnetic Field

• A current carrying wire experiences a force if it is placed at a non 0 angle to the lines of force of an external magnetic field - MOTOR EFFECT

• Force is greatest when wire is at right angles to the field lines

• Force is zero when parallel to the magnetic field

• Increase I, Increase Force

• increase L, increase force

B = Magnetic Flux density = Strength of magnetic field OR force per unit length per unit current on a conductor at right angles to the field OR how many field lines there are in a region (so increase B = increase Field Strength)

F = BILSinθ

Moving Charges in a Magnetic Field

• A beam of charged particles crossing a vacuum tube is the same as a current

• So there is a magnetic field generated

• So there is a force on the particle

F = BQv

Charged Particles in Circular Orbits

• No work is done by the magnetic field on the particle, as the force always acts at right angles to the velocity of the particle. So the direction of motion is changed by the force, but not its speed. The KE of the particle is also unchanged.

• Because Force of Magnetic field is always at right angles to the velocity - the particle moves in a circular path - force always acts to the centre of its path

• So there is a centripetal acceleration

Radius ‘r’ of orbit depends on B and v of particles

F = BQv and F = Mv²/r, combining the two gives

r = mv/BQ

• Increase V = increase r

• Decrease B = increase R

• Use particles of larger Q/m ratio = decrease r

Electromagnetic Induction

• If a wire cuts and disrupts the field lines of a magnetic field - emf is induced in the wire

• TO INDUCE THE EMF THERE HAS TO BE RELATIVE MOVEMENT BETWEEN THE WIRE AND THE MAGNETIC FIELD

• If the wire is connected into a complete circuit - an induced current can flow

• Increase speed of movement of wire = increase emf

• Increase strength of magnet = increase emf

• Making the wire into a coil/increasing number of coils = increase emf

if wire is parallel to magnetic field lines as it moves through the field - no induced emf

Energy Changes

• Induced EMF rises to a maximum, and a minimum (0) relative to the motion of the wire. IF THE WIRE STOPS MOVING, EMF DROPS TO 0

Lenz’s Law

• THE DIRECTION OF THE INDUCED CURRENT IS ALWAYS SUCH AS TO OPPOSE THE CHANGE THAT CAUSES THE CURRENT

• If the current was directed in the same way as the change that caused it, then the current is helping the change that caused it, and hence producing electrical energy from nothing - IMPOSSIBLE DUE TO CONSERVATION OF ENERGY!

Faraday’s Law

• emf = BA/Δt

• BA = flux density x Area = magnetic flux (shown by Φ)

• Magnetic Flux Linkage = NΦ = BAN (total amount of flux)

• Φ is measured in Webbers, Wb

• NΦ = BAN if magnetic field is perpendicular to the coil fail

• If magnetic field is parallel to the coil area, flux linkage = 0

• NΦ = BANCosθ

FARADAY’S LAW STATES THAT THE INDUCED EMF IN A CIRCUIT IS EQUAL TO THE RATE OF CHANGE OF FLUX LINKAGE THROUGH THE CIRCUIT

emf = -NΔΦ/Δt (negative to show that the induced emf acts in the opposite direction to oppose the change that causes it as per Lenz’s law)

THERE HAS TO BE A CHANGE IN FLUX LINKAGE IN ORDER TO INDUCE AN ELECTROMOTIVE FORCE