It works because of the force produced by the motor effect on the free electrons in a conductor: v B The size of the force on the electrons due to their movement through the ‘B’ field is: The motor effect will cause the electrons (negative charge) to move in the direction shown. FBFB This will cause an uneven distribution of charge in the wire, so an ‘E’ field will be set up which pushes the electrons in the opposite direction to the ‘B’ field. FEFE How does electromagnetic induction work ? Consider a wire moving downwards through a ‘B’ Field which is across the page as shown: The free electrons in the wire are moving downwards because... This is movement of charge which constitutes a...current the wire is moving downwards. When there is a current in a ‘B’ field, there is a force because of...The motor effect The force produced on each electron by this ‘E’ field will be given by: In the direction shown. 2 nd Finger (Current) 1 st Finger (Field) (Thumb) Force on +ve charge

But the Electric Field Strength ‘E’ can be given in terms of the Voltage across the wire by: So F E becomes: F E and F B will balance, so we can say: or But ‘V’ is the Voltage induced in the wire, or the EMF. So, for a wire moving through a magnetic field : Magnetic Field Strength Length of wire in Magnetic Field Velocity of wire. Where ‘l’ = length of the wire from

Predicting the direction of the induced emf. From first principles: v B FBFB FEFE Shortage of electrons here So this end is positive Surplus of electrons here So this end is negative So current flows this way in the wire (Negative to positive as inside a battery) Use Flemings Left Hand Rule for Motor effect Use Flemings Right Hand Rule for Generator effect Current flows from + to – in the external circuit

A new quantity : ‘  ’, the Magnetic Flux We already have Magnetic Field Strength ‘B’ = Force per unit current and unit length Now we introduce a new quantity: Flux ‘  ’=‘Amount of ‘magnetic field through a certain area’  For uniform fields: Units for ‘B’ are...Tesla (T) Units for ‘  ’ are... Webers (Wb)  1 T = 1Wb m -2 Magnetic Field Strength can now also be called ‘Flux Density’ or We can also obtain the definition of Magnetic Flux from the above formula: The magnetic flux through a small plane surface is the product of the flux density normal to the surface and the area of the surface.

If the conductor moves a distance Δx in time Δt, then its velocity is: A conductor must always be considered as part of a complete circuit if the EMF across it is to be either measured or used to drive a current. The area of flux enclosed by this loop is called the ‘Flux Linkage’ ‘F’. Now consider the change in Flux Linkage as the conductor moves through the field. NS l xx AA V Sobecomes ButSo ButSo

This is Faraday’s Law: The magnitude of the induced emf in a circuit is directly proportional to the rate of change of flux linkage with the circuit. We have arrived at a ‘formula’ with an ‘=‘ sign, whereas Faraday’s law only uses the word ‘proportional’ why ? Consider what would happen if we had a small resistance in the loop rather than a voltmeter. 1. Moving the wire through the field would induce an emf. 2. This would cause a current to flow, which would produce a motor effect 3. This would cause the wire to move faster which would produce a bigger emf. 4. This would cause a bigger current which would cause a bigger motor effect etc.. We would have a perpetual motion machine ! This is impossible, and leads to Lenz’s Law: The direction of the induced emf is always such that the current it causes opposes the change which produces it. Faraday’s Law and Lenz’s laws combined give: The ‘missing’ constant is the ‘-1’ imposed by Lenz’s Law For a coil of ‘N’ loops

It works because of the force produced by the motor effect on the free electrons in a conductor: v B The size of the force on the electrons due to their movement through the ‘B’ field is: The motor effect will cause the electrons (negative charge) to move in the direction shown. This will cause an uneven distribution of charge in the wire, so an ‘E’ field will be set up which pushes the electrons in the opposite direction to the ‘B’ field. How does electromagnetic induction work ? Consider a wire moving downwards through a ‘B’ Field which is across the page as shown: The free electrons in the wire are moving downwards because... This is movement of charge which constitutes a... the wire is moving downwards. When there is a current in a ‘B’ field, there is a force because of... The force produced on each electron by this ‘E’ field will be given by: In the direction shown. 2 nd Finger (Current) 1 st Finger (Field) (Thumb) Force on +ve charge

But the Electric Field Strength ‘E’ can be given in terms of the Voltage across the wire by: So F E becomes: F E and F B will balance, so we can say: or But ‘V’ is the Voltage induced in the wire, or the EMF. Where ‘l’ = length of the wire from

Predicting the direction of the induced emf. From first principles: v B FBFB FEFE Shortage of electrons here So this end is positive Surplus of electrons here So this end is negative So current flows this way in the wire (Negative to positive as inside a battery) Current flows from + to – in the external circuit

A new quantity : ‘  ’, the Magnetic Flux We already have Magnetic Field Strength ‘B’ = Now we introduce a new quantity: Flux ‘  ’=  For uniform fields: Units for ‘B’ are... Units for ‘  ’ are... Magnetic Field Strength can now also be called ‘Flux Density’ or We can also obtain the definition of Magnetic Flux from the above formula:

If the conductor moves a distance Δx in time Δt, then its velocity is: A conductor must always be considered as part of a complete circuit if the EMF across it is to be either measured or used to drive a current. The area of flux enclosed by this loop is called the ‘Flux Linkage’ ‘F’. Now consider the change in Flux Linkage as the conductor moves through the field. NS l xx AA V Sobecomes ButSo ButSo

This is Faraday’s Law: We have arrived at a ‘formula’ with a ‘=‘ sign, whereas Faraday’s law only uses the word ‘proportional’ why ? Consider what would happen if we had a small resistance in the loop rather than a voltmeter. 1. Moving the wire through the field would induce an emf. 2. This would cause a current to flow, which would produce a motor effect 3. This would cause the wire to move faster which would produce a bigger emf. 4. This would cause a bigger current which would cause a bigger motor effect etc.. We would have a perpetual motion machine ! This is impossible, and leads to Lenz’s Law: Faraday’s Law and Lenz’s laws combined give: For a coil of ‘N’ loops