Faraday's Law
Brook Edgar
Teacher
Explainer Video
Faraday's Law
When the magnetic flux linkage passing through a conductor changes, an emf is induced in the conductor; Faraday’s Law explains this.
Formula:
The emf induced is directly proportional to the rate of change of magnetic flux linkage.
Faraday's law can be shown when a magnet is pushed into a coil of wire. The number of magnetic field lines cutting the cross-sectional area of the coil increases as the magnet is pushed in; this rate of change of magnetic flux linkage across the conductor induces a potential difference in the coil. If it is a complete circuit, a current will flow.
When a potential difference is induced in the coil and a current flows through the coil, a magnetic field is created around the coil of wire that acts to oppose the change that caused it. This is Lenz’s Law, often represented by a negative sign in front of Faraday's Law:
When a north pole from the permanent magnet is pushed into the coil, a north pole is induced at that end of the coil to oppose the incoming north pole, as shown in the image above; this ensures conservation of energy. When pulling the magnet away - the opposite occurs.
Remember: Current flowing through a wire induces a magnetic field around the wire, with the direction indicated by the right-hand rule. When the wire is wrapped into a solenoid, the solenoid rule can be used to determine the polarity of the magnetic field at that end of the coil. 
Worked Example
Grace has a wire coil of turns, radius , held in a magnetic field, strength . The magnetic field is removed completely in .
Calculate the emf induced in the coil.
Answer:
Teacher Tips: To calculate the magnetic flux it is the product of magnetic field strength and the cross sectional area of the coil, .
Worked Example
A magnet is displaced vertically and released so it oscillates. The vertical component of the magnetic flux density through the coil varies at a maximum rate . The radius of the copper ring is and the resistance of the copper ring is . Calculate the maximum current in the copper ring.
Answer:
Teacher Tips: The coil is circular, so the cross-sectional area is that of a circle -> . The question provided the rate of change in magnetic flux, so .
Practice Questions
Describe how the reading on an ammeter changes as a bar magnet is moved towards a coil of wire and brought to rest.
-> Check out Brook's video explanation for more help.
Answer:
Magnetic field lines cut the coil. The rate of change of magnetic flux linkage increases as the magnet moves into the coil, inducing an emf in the coil.
If it is a complete circuit, a current flows and is detected on the ammeter. The reading returns to zero when the magnet stops moving, as there is no longer any change in magnetic flux linkage.
takes longer to pass through the metal tube than . Explain why, knowing that is magnetised, steel is a strong permanent magnet.
-> Check out Brook's video explanation for more help.
Answer:
falls slower as it is magnetic. As the magnetic field from the moving magnet cuts through the copper tube, a rate of change of magnetic flux linkage occurs, inducing an emf in the copper tube.
The emf in the copper tube produces a current, which then produces a magnetic field in the copper tube that repels the incoming magnetic field from due to Lenz’s law. This causes to slow down as it has a force opposing its motion.
is not magnetic, so current is not induced in the copper tube and, therefore, no opposing magnetic field is created, so no repulsive force is experienced.