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Flux and flux density
 Inducing a current
 We have seen that we can induce an EMF by changing the amount of magnetic field in a circuit. We can do this by moving a wire through a magnetic field or moving a magnet near to a coil. But what do we mean by amount of magnetic field?
 4.11 We can change the flux in a circuit by moving a wire or changing the field strength.
 Magnetic flux Picture 4.11 shows a wire moving through a magnetic field. We represent the magnetic field with magnetic field lines (in this case, they are going into the screen and are shown as crosses). As the wire moves through the field, the number of field lines enclosed by the circuit increases. So the total field in the circuit has gone up. We call this the magnetic flux. It has the symbol f - (phi to rhyme with fly). There is another way of increasing the flux in the circuit: make the field stronger. This is like bringing a magnet closer to the circuit. So the flux in the circuit changes whether we: move the wire in a steady field or change the field. And in each case, we get an induced EMF.
 Magnetic flux density You can think of the flux as being represented by the number of field lines. We sometimes call them lines of magnetic flux. The closer together the lines of flux, the stronger the field. That is, the strength of the field is represented by the density of the lines of flux. We sometimes call the magnetic field strength, B, the magnetic flux density. And we use this idea to define flux:
 Faraday's Law We have seen that the faster we move a wire, the bigger the EMF we induce. In fact, we find that the EMF is proportional to the rate at which the flux changes. So, in a simple circuit: This means that if we double the speed of the wire, the flux in the circuit increases at twice the rate. Therefore, the EMF is twice as big. We can increase the total flux linking a circuit by using a coil rather than a single piece of wire. In which case, the EMF, E, will increase in proportion with the number of coils, N. So we get an expression for Faraday's Law: Notice the minus sign in the equation. This is to indicate that the induced EMF opposes the change in flux that produced it.
 4.12 See question 14.
 4.13 See question 14 part f.
Question 14
 Look at the circuit in picture 4.12. It shows a wire moving through a magnetic field. The wire is attached to a voltmeter. The magnetic flux density is 2 tesla and the wire is moving at 3 cm s-1. The length of the wire is 20 cm. Imagine we start timing the moving wire when it is 10 cm into the field. a) What is the area of magnetic flux passing through the circuit? b) How much flux is passing through the circuit? c) After 5 seconds, the wire will have moved through the field. How far will it have moved? d) By how much will the flux have increased in those 5 seconds? e) What is the EMF induced in the wire? Imagine that we now move the whole circuit through the field (picture 4.13). f) What will the voltmeter reading? g) Explain your answer.