Summary
Faraday's law gives the magnitude of the EMF induced due to a change in flux. Lenz's law tells us the direction.
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Definition
Lenz's law states that the direction of the induced current is such that it will oppose the change producing it. This means that we can now state the equation for the induced EMF:
\(\varepsilon =-{\mathrm{d}N\Phi\over \mathrm{d}t}\)
- \(\varepsilon \) is the induced EMF (V)
- \(N\Phi\) is the magnetic flux linkage (Tm2 or Wb)
- \({\mathrm{d}N\Phi\over \mathrm{d}t}\) is the rate of change of magnetic flux linkage (Tm2s-1 or Wb s-1)
Sliding wire
To fully understand the cause of Lenz's law, we must consider the motion and forces exerted by individual charges.
Conservation of energy
Lenz's law is a consequence of Conservation of energy. An induced EMF does work on charges causing them to move in a net direction (and hence for a current to flow).
The induction of current requires energy. Therefore, either:
- work must be done to continue the relative motion of the magnetic field and conductor
- the conductor or magnet will lose kinetic energy so that the EMF induced decreases
Stretch for 7
Induced EMF direction
Lenz's law has implications for any instance of electromagnetic induction. There are two mechanisms for determining the direction of the EMF:
- Consider the direction in which individual moving charges experience a force. This is directed by Fleming's left hand rule.
- Consider the direction in which EMF is induced by a conductor moving relative to a magnetic field. The switch to the right hand rule incorporates the opposing nature set by Lenz's law.
It can sometimes be difficult for learners to work out the EMF direction because of uncertainty in whether to consider individual charges or the whole of the conductor.
The good news is that there is a simple solution: since we know the consequence of Lenz's law is to oppose the change producing it, the resulting electromagnet formed will always:
- repel an incoming magnetic field
- attract an outgoing magnetic field
Falling magnet
When a magnet falls through a conductor, the current direction in the conductor is such as to exert an upward force on the magnet.
Coil and magnet
When a magnet moves towards a coil, the current direction in the coil is such as to repel the approaching magnet.
If a north pole moves to the right towards a coil, the coil will become an electromagnet with a north pole on its left.
The right hand grip rule can be used to verify that the direction of conventional current would do so. Note that the current in the side of the coil nearest the reader is upward.
Coil in a changing field
When a coil is placed next to an electromagnet coil, the field produced by the induction in the second coil will be in the opposite direction to the field produced by the first coil.
Eddy currents
Eddy currents are induced within a conductor. They flow in closed loops that is perpendicular to the magnetic field. These currents themselves cause the conductor to become an electromagnet.
Eddy currents cause dissipation of thermal energy in devices that employ electromagnetic induction. This can be useful in braking but wasteful in generators and transformers. One mechanism to reduce eddy currents is to laminate any soft iron core present.
Test yourself
Use quizzes to practise application of theory.
START QUIZ!
A conducting ring passes through the magnetic field as shown.
The induced current will flow:
We can use Fleming's right hand rule to determine the directions of the current.
As the bottom of the ring enters the field it is moving downwards and the field is into the page. Conventional current is to the right and so flows anti-clockwise.
As the top of the ring leaves the field it is moving downwards and the field is into the page. Conventional current is to the right and so flows clockwise.
A conducting ring passes through a magnetic field as shown.
The induced current will flow:
We can use Fleming's right hand rule to determine the directions of the current.
As the right of the ring enters the field it is moving to the right and the field is into the page. Conventional current is upward and so flows anti-clockwise.
As the left of the ring leaves the field it is moving to the right and the field is into the page. Conventional current is upward and so flows clockwise.
A conducting ring passes through a uniform magnetic field at constant speed as shown.
What can be said about the induced current?
There is no change in flux as the magnetic field and the velocity of the ring are constant. Therefore there is no induced EMF (depends on rate of change of flux) and so no induced current.
A metal bar passes through a magnetic field as shown.
Which statement is true about the charge at the ends of the bar?
In this case we use Fleming's left hand rule to determine the direction of force on each free electron. The bar containing the electrons moves downwards, so conventional current is upward. The field is into the page. The force on an electron is to the left and so the left side of the bar will become negative (leaving a net positive charge on the right)
A conductor of length \(l\) travels with velocity \(v\) through a magnetic field of flux density \(B\).
What is the magnitude of the induced EMF?
The EMF is equal to the flux cut per unit time: \(Blvt\over t\)
Two magnets are dropped through two coils as shown.
As the magnets enter the coils, the EMF induced reaches a maximum. If the maximum value across the left hand coil is \(\varepsilon\), what is the EMF across the right hand coil?
All factors including field strength and speed are the same except for the number of turns on the coil:
\(\varepsilon\propto N\)
Two magnets are dropped through two short circuited coils as shown.
As the magnets enter the coils, the current induced reaches a maximum. If the maximum current in the left hand coil is \(I\), what is the current in the right hand coil?
The size of the induced EMF is double for the right hand coil as the number of turns has doubled. However, the right hand coil is twice the length and so will have double the resistance.
Since \(I={V\over R}\), the current is the same.
Two magnets are dropped into two identical coils. The magnet on the left is twice as high above the coil as the one on the right.
As the magnets enter the coils, the EMF induced reaches a maximum. If the maximum value in the left hand coil is \(E\), what is the maximum EMF in the right hand coil?
\(E\) is proportional to the magnet's velocity when it enters the coil.
Using equations of uniformly accelerated motion or conservation of mechanical energy, \(v^2 = 2as\):
\(v\propto \sqrt s \)
A square coil with \(N\) turns and area \(A\) is positioned in a field of flux density \(B\) as shown:
The flux enclosed is:
The component of the flux denity perpendicular to the plane of the coil is \(B\sin a\).
It is always worth scrutinising angles that you are given in diagrams rather than blindly using \(\sin\) or \(\cos\) as suggested in the Data Booklet.
Which of the following is not a unit of magnetic flux density?
T is the SI derived unit of magnetic flux density.
NA-1m-1 is from the equation \(F=BIl\) for the magnetic force exerted on a current-carrying conductor.
NC-1m-1s is from the equation \(F=Bqv\) for the magnetic force exerted on a charge. Therefore, NCms-1 cannot also be accurate.
The graph represents the changing flux density in a coil.
If the EMF induced in the coil is 2V when the flux changes at the rate of line A, what will the EMF be if the flux changes at the rate of line B?
EMF is proportional to the rate of change of flux. The gradient of B is \(1\over 6\) of the gradient of A, so EMF will be \({1\over 6} \times 2\) .
Two magnets are dropped into two coils. The magnet on the left is twice as high above the coil as the one on the right.
As the left magnet passes into its coil the current induced reaches a maximum value \(I\). What is the maximum current in the right hand coil?
A close inspection of the diagram reveals that the right hand coil is open - no current can flow!
Had the circuit been shorted like the first, the size of the maximum current would have been \(I\over \sqrt2\).
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