Induced Emf (HL) (HL IB Physics)

• Electromagnetic induction is a phenomenon which occurs when an e.m.f. is induced due to relative movement between a conductor and a magnetic field

• This could occur when:
  • a conductor moves relative to a magnetic field
  • a magnetic field varies relative to a conductor

• When a conductor cuts through magnetic field lines:
  • the free electrons in the conductor experience a magnetic force
  • this causes work to be done as charges in the conductor become separated
  • mechanical work is transferred to the charges as electric potential energy
  • a potential difference is created between the ends of the conductor, or in other words, an e.m.f. is induced

• This induced e.m.f. is defined as:

The amount of work done per unit charge in separating the charges to the ends of a conductor

• If the ends of the conductor are connected to a closed circuit, an induced current will be able to flow
• Therefore, we can define electromagnetic induction as:

The process in which an e.m.f or current is induced in a closed circuit due to changes in magnetic flux

• To induce a current in a straight current-carrying conductor in a magnetic field
  
  • it must be placed in a perpendicular field, so when it moves it cuts the magnetic field lines
  • the closed circuit must be positioned outside of the field, so the e.m.f. is induced across the conductor in the field only, and not the entire circuit (which would mean no current flow)

Conducting rod moving perpendicular to a magnetic field directed into the page

• The induced e.m.f in the conductor, as it moves through the magnetic field, is:

• Where:
  • ε = induced e.m.f. (V)
  • B = magnetic flux density (T)
  • L = length of the conductor in the field (m)
  • v = velocity of the conductor travelling through the field (m s^–1)

• This equation shows that the size of the induced e.m.f increases if:
  • the length of the conductor in the field is increased
  • the magnetic field strength is increased
  • the conductor cuts through the field lines faster

• Coiling a wire to form many loops or turns, will also increase the size of the induced e.m.f.
• For a coil moving through a magnetic field, the induced e.m.f. is:

• Where N = number of turns on the coil

• The phenomenon of EM induction can be demonstrated using a magnet and a coil, or a wire and two magnets

Experiment 1: Moving a magnet through a coil

• When a coil is connected to a sensitive voltmeter, a bar magnet can be moved in and out of the coil to induce an e.m.f

A bar magnet is moved through a coil connected to a voltmeter to induce an e.m.f

The expected results are...

1. When the bar magnet is not moving, the voltmeter shows a zero reading

• • When the bar magnet is held still inside, or outside, the coil, the rate of change of flux is zero, so, there is no e.m.f induced

2. When the bar magnet begins to move inside the coil, there is a reading on the voltmeter

• • As the bar magnet moves, its magnetic field lines ‘cut through’ the coil, generating a change in magnetic flux (ΔΦ)
  • This induces an e.m.f within the coil, shown momentarily by the reading on the voltmeter

3. When the bar magnet is taken back out of the coil, an e.m.f is induced in the opposite direction

• • As the magnet changes direction, the direction of the current changes
  • The voltmeter will momentarily show a reading with the opposite sign

4. Increasing the speed of the magnet induces an e.m.f with a higher magnitude

• • As the speed of the magnet increases, the rate of change of flux increases

An e.m.f is induced only when the bar magnet is moving through the coil

• Factors that will increase the magnitude of the induced e.m.f are:
  • Moving the magnet faster through the coil
  • Adding more turns to the coil
  • Increasing the strength of the bar magnet

Experiment 2: Moving a wire through a magnetic field

• When a long wire is connected to a voltmeter and moved between two magnets, an e.m.f is induced
  • Note: there is no current flowing through the wire to start with

A wire is moved between two magnets connected to a voltmeter to induce an e.m.f

The expected results are...

1. When the wire is not moving, the voltmeter shows a zero reading

• • When the wire is held still inside, or outside, the magnets the rate of change of flux is zero so there is no e.m.f induced

2. As the wire moves between the magnets, an e.m.f is induced within the wire

• • This is shown momentarily by the reading on the voltmeter
  • As the wire moves through the magnetic field, it ‘cuts through’ the magnetic field lines, generating a change in magnetic flux

3. When the wire is moved back out of the field, an e.m.f is induced in the opposite direction

• • As the wire changes direction, the direction of the current changes
  • The voltmeter will momentarily show a reading with the opposite sign

• Factors that will increase the magnitude of the induced e.m.f are:
  • Increasing the length of the wire
  • Moving the wire between the magnets faster
  • Increasing the strength of the magnets