magnetic fields

• a magnetic field is a region of space around a magnet when a magnetic force can be experienced by magnetic or magnetically susceptible materials (eg iron).
• a magnetic force can be attractive or repulsive
• X = current flowing away from you
• • = current flowing towards you
• the motor effect is the phenomenon of a force being generated on a current-carrying wire in the presence of an external magnetic field
• the direction of a force is always perpendicular to both the external field and the current
• magnetic flux density B is the force on 1 metre of current-carrying wire of 1 amp at right angles to the external magnetic field
• the magnitude of the force on a current carrying conductor depends on the angle of the conductor to the external B field
• F = BIL

  where L is the length of wire within the field
• the direction of the force on a current carrying conductor in a magnetic field can be found using Fleming's left hand rule
• magnetic flux density is measured in teslas
• a magnetic flux density of 1 tesla is equal to one newton per amp per metre
• a moving charge in a magnetic field experiences a force due to the motor effect at 90 degrees to both the magnetic field and the velocity of the charge. this causes the charge to follow a curved path with the force directed towards the centre
• mass spectrometers allow charged particles of different masses/charges to be separated since they will follow different paths when travelling in the same magnetic field
• cyclotron

  a uniform magnetic field perpendicular to the plane of these dees

  small gap separates the dees

  charged particles are directed into of the dees near the centre of the cyclotron and are forced to move in a circular path inside the dee. no work is done, the speed of the particles is constant

  when the particles cross the gap, the alternating voltage reverses so that they are attracted to and accelerated towards the other dee. they gain energy equal to Qv and accelerate to the next dee

  every time the particles cross the gap they are accelerated

  the particles are ejected with a high energy
• this equation proves that the time spent in each dee does not depend on either the radius or the speed

  $t=$$πm/BQ$
• the hall probe is used to measure the magnetic flux density between two magnets based on the Hall effect
• split-ring conductor: rotate with the coil and provide points of electrical contact between the applied pd source and the coil. every 180 degree contact swaps polarity of the contacts and the current direction reverses. this means the motor effect forces continues to cause rotation in the same direction
• an electromotive force (EMF) is induced in a conductor if there is relative movement between the conductor and the lines of magnetic flux which "cuts" the lines of flux
• moving the conductor without cutting across any flux lines, no emf is induced if the conductor moves parallel to the field lines
• if the conductor is part of a complete circuit, the induced emf forces electrons around the circuit. a current is generated. this is refered to the generator effect
• a motor (a device that relies on the motor effect to generate motion) can be used in reverse to generate an induced emf
• the magnetic field lines pass through a current carrying solenoid from one end (the north pole) to the other end (the south pole). we can assign the north/south poles (and therefore the direction of the field according to the following: current passes anticlockwise around the north pole
• Lenz's law states that the direction of the induced current/emf is always such as to oppose the change that causes the current/emf
• a graph of an object leaving the coil should have a higher peak emf as it is travelling faster and will cut more field lines
• the magnetic flux Φ is the product of the magnetic flux density B and the cross-sectional area A that is perpendicular to the direction of the magnetic flux density

  $Φ=$$BA$
• magnetic flux linkage is a quantity used for solenoids made from N turns of wire. it is defined as the product of magnetic flux and the number of turns of the coil.

  $NΦ=$$BANcosθ$
• magnetic flux linkage is measured in weber-turns
• a change in flux linkage of one weber per second will induce an emf of 1V in a loop of wire
• the angle between the normal and the B field

  $Φ=$$BAcosθ$
• the angle between the B field and the coil

  $Φ=$$BAsinθ$
• Faraday's law is defined in terms of a coil of N turns and states that the magnitude of the induced emf in a circuit is equal to the rate of change of flux linkage through the circuit

  $ε=$$-N ∆Φ/∆t$

  where the minus sighn represents lenz's law
• ε = N ∆Φ/∆t = ε = BA/∆t = ε = Bl∆s/∆t

  ∆s/∆t = v

  ε = Blv
• the magnitude of the emf is shown by the gradient of a graph of flux linkage against time
• the simple ac generator consists of a rectangular coil that spins in a uniform magnetic field. as the coil rotates the flux linkage varies continuously and so therefore does the induced emf
• assuming that the coil is rotating with a frequency, the angle θ between the normal to the plane of the coil and the magnetic field can be related to the rotational motion:

  θ=2πft

  NΦ=BANcos2πft or NΦ=BANcosωt

  ε=N∆Φ/∆t then ε=BANωsinωt
• peak emf = BANω = 2NBlv
• it can be shown mathematically that the induced emf alternates according to the equation

  ε = ε0sinωt
• back emf acts against pd supplied by the motor

  this is in accordance with lenzs law

  V-ε =IR
• induced emf is proportional to the speed of rotation of the motor. current changes as the motor speed changes

  at low speed, current is high because induced emf is small

  at high speed, current is low because induced emf is large