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Magnet Fields. 5.14 Magnetic Flux. 5.15 Electromagnetic Induction 5.16 Magnetic Effect of a Steady Current. 5.14 Magnetic Flux. Magnetic flux flux linkage. = BA. Magnetic Flux. The magnetic flux is a measure of the number of field lines passing through a region.
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Magnet Fields 5.14 Magnetic Flux. 5.15 Electromagnetic Induction 5.16 Magnetic Effect of a Steady Current
5.14 Magnetic Flux • Magnetic flux • flux linkage. • = BA
Magnetic Flux • The magnetic flux is a measure of the number of field lines passing through a region. • The unit of magnetic flux is the weber (Wb) • It is a vector quantity A A uniform magnetic field has a constant density of field lines throughout In a uniform field the number of field lines passing through the larger region B is greater than through the smaller region A. Therefore we can say that there is a greater flux through B than A B
Magnetic Flux Here the magnetic flux is the same in region A and B. Sometimes a measure of magnetic flux can be misleading.
Magnetic Flux • Below the magnetic flux through region A is greater than through B because the density of the field lines is greater. A B
Magnetic flux density • The magnetic flux density is represented by the symbol B. • It is measured in Tesla (T). • It is a measure of the flux per square metre. • This enables us to compare the field strength
Magnetic Flux • Definition: • Magnetic field lines are lines of magnetic flux. • The product between the magnetic flux density and the area when the field is at right angles to the area. • The area can be thought of as the area swept out by a conductor. • Symbol: • Equation: = BA • Units: Wb (Weber) or Tm2 • Note: • The magnetic field strength is also known as the Magnetic Flux Density. • Magnetic Flux Density = Magnetic Flux Area thus Magnetic Flux = Magnetic Flux Density x area
Magnetic Flux Linkage • When we are dealing with stationary conductors in changing magnetic fields, we often work with loops and coils of wires.
Simply treat each loop of the coil as if it was on its own. Hence, if you have 'n' loops in the coil you have 'n' times the area and therefore 'n' times the flux. • This is called flux linkage, F.
Flux Linkage • If each turn cuts (or links) flux , the total flux linkage for N turns must be N . • We can also write this as NBA. • Flux linkage = number of turns of wire x magnetic field strength x area • The flux linkage can be changed in two ways: • We can alter the strength of the magnetic field; • We can alter the area at 90° to the magnetic field by moving the coil.
Electromagnetic Induction • Experimental demonstration that change of flux induces an e.m.f. in a circuit. • Data logging: V against t as a magnet falls through coil. • Faraday’s and Lenz’s laws of electromagnetic induction. • e.m.f. as equal to rate of change of magnetic flux linkage. • Lenz’s law as illustrating energy conservation. • = N/t • Investigations: • Faraday’s law - variation of with N and rate of change of B.
Inducing a Voltage: Moving Conductor • As you swipe the metal bar to the left you sweep through the area of field shown by the crosses. • It’s this movement through a field that induces (produces) an e.m.f. across the bar ends.
Increasing the Induced EMF • A longer bar would ‘sweep’ out more area of field. • A strongerfield would mean you swept through more field lines when moving the same distance. • A faster swipe would mean you swept out more area of the field per second.
Method 2: Changing the Field • Changing the Magnetic Field Around a Conductor. i.e. moving a magnet in a coil. • Increasing the Induced EMF: • More turns • Stronger field • Quicker changing field
Faraday’s law • Used to find magnitude of induced emf • “an induced emf is directly proportional to rate of change of flux linkage or flux cutting” • i.e. - d(N) dt • i.e. to increase the e.m.f. you can: • increase the number of turns • the amount of flux through the coil • the rate of change of the flux (speed of magnet or change of magnetic field)
Experimental Proof of Faraday’s Law • Investigate changing frequency and number of turns on second coil on induced emf • Conclusions: • Increase frequency or Number turns on secondary coil increases the induced EMF
Definition of Weber: the magnetic flux that induces in a 1 turn coil an emf of 1 volt when the flux is reduced to zero in 1 second • Hence constant of proportionality = 1 • = - N d or = -N dt t
Demo • Hovering Aluminium Ring
Lenz’s law • The direction of any induced current is such as to oppose the flux change that caused it • i.e. if you induce a current it will create a magnetic field to oppose the motion that made it – otherwise you would be getting energy for free! • Used to find direction of induced e.m.f. • This e.m.f. is often called the back e.m.f as it opposes any flowing e.m.f. on a coil (e.g. a motor)
Effects of Lenz’s Law • Demo: Aluminium Ring through a magnet. • What will happen? • Why does it not work in both rings? • Demo: Magnet down Cu or Al pipe
Remember • LEFT hand for motor effect of a magnetic field • RIGHT hand for generator effect (induced magnetic field)
The Transformer • The transformer. Explained in terms of magnetic flux linkage. • For an ideal transformer: Vp/Vs = Np/Ns • Investigation: number of turns and output voltage.
Theory • A.C. in a coil will set up a changing magnetic field in the coil, which will mean that the core becomes a constantly changing magnet. • Put a second coil around this changing magnet (the core) and you induce an alternating e.m.f. in the coil.
Transformers • We name the first coil the primary coil and the second coil the secondary coil. • If you change the number of turns in the coils you change the induced emf. • This allows you to change (transform) the voltage from the primary to the secondary coil.
Turns Rule Ns = Vs Np Vp • Where: • Ns = number of turns on the secondary coil • Np = number of turns on the primary coil • Vs = voltage across the secondary coil • Vp = voltage across the primary coil • So if number of turns on the secondary coil is greater than on the primary coil, the output voltage will be greater than the input voltage. • This is called a step up transformer.
Why Transform the Voltage To deliver 10kW at 100V, the current needed is: P = IV I = P ÷ V I = 10000 ÷ 100 = 100A What is the effect of 100A travelling through a copper wire? P = I2R = 1002 X 100 = 1 MW Thus to supply 10 kW of power you waste 1 MW as heat
Raising the Voltage If we increase the voltage to 10 kV during transmission, the current needed is: P = IV I = P ÷ V I = 10000 ÷ 10000 = 1A What is the effect of 1A travelling through a copper wire? P = I2R = 12 X 100 = 0.1 kW Thus to supply 10 kW of power you waste 100 W as heat
Efficiency of Transformers • Transformers, however, are not 100 % efficient. • Energy is lost in the wires in the coils and in the iron core itself. • You can notice this with transformers in the home – on your mobile charger for instance. • Small eddy currents are induced in the iron core, which waste energy heating up the core. • Eddy currents can be reduced by laminating the core - for instance, by making the core out of thin slices of metal, which are ‘glued’ together.
Electromagnetic induction 13.4.4
