In the SL Magentism course, you will have studied the motor effect, in which a current-carrying conductor or moving charge experiences a force in a magnetic field.
In the HL course, we move to electromagnetic induction. When a magnetic field is changed or moved relative to an electrical conductor, an EMF is induced. When the conductor is connected as part of a complete circuit, a current flows.
Faraday's law enables us to calculate the size of the induced voltage. First we will need to define a new concept - magnetic flux.
Key Concepts
When a charge moves in a magnetic field, it experiences a force that is perpendicular to its velocity. This causes free charges to move in a circular path (NB: Centripetal force). The direction of this force can be determined using Fleming's left hand rule:
However, when constrained to a linear electrical conductor (i.e. a metal wire), charges cannot follow a circular path. If the wire continues to move in a straight line, electrons all electrons will experience a force in the same direction and move. Now that the electrons are not distributed evenly throughout the conductor, the wire has an electric field across it (like a battery). An EMF has been produced, that would cause a current to flow if the wire was connected to a resistor in a complete circuit.
Instead of having a plane area within the field, the alternative is a length of wire that sweeps through it.
\(\varepsilon=BLv\sin\theta\)
- \(\varepsilon\) is the EMF induced (V)
- \(B \) is magnetic flux density (T)
- \(L\) is the length of wire (m)
- \(v\) is the velocity of the wire (ms-1)
- \(\theta\) is the angle between the magnetic field lines and the normal (perpendicular) to the swept out area
The EMF induced is constant. A real-world example is a plane flying through the Earth's magnetic field!
The subject guide suggests that all cases of a wire moving through the field will be at right angles. But there's no harm in being prepared!
It is interesting, but not essential, to know how to derive Faraday's law. You should revise AHL electric potential beforehand.
To do so, consider a metal wire. At the point at which the electric force acting on electrons (to return them to their evenly distributed state) is equal to the magnetic force (causing them to move to one side):
\(F_B=F_E\)
\(Bev=Ee\Rightarrow Bev={V\over L} e\)
\(V=BLv\)
- \(V\) is the work done per unit charge against the electric force by the magnetic force (V)
- \(B\) is magnetic flux density (T)
- \(L\) is the length of the conducting wire (m)
- \(v\) is the velocity at which the wire moves through the field (ms-1)
Since the work done per unit charge in bringing the charges to their induced position is equal to that which would be released when a complete circuit is formed:
\(\varepsilon = BLv\)
- \(\varepsilon\) is the induced EMF (V)
Or if the wire is replaced by a coil with multiple turns:
\(\varepsilon=BLvN\)
- \(N\) is the number of turns in the coil
How much of Faraday's law have you understood?