FARADAY S AND LENZ LAW B O O K P G


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1 FARADAY S AND LENZ LAW B O O K P G
2 MOTIONAL EMF AND MAGNETIC FLUX (DERIVIATION) Motional emf = vbl Let a conducting rod being moved through a magnetic field B During time t 0 the rod has been moved to the right a distance x 0 At a later time t, the rod has moved an even greater distance x t =0s t 0 = 0.02s A 0 A The speed of the rod is given by v = s t x 0 x
3 v = s t v = x x 0 substitute into emf = vbl Emf = x x 0 BL = xl x 0L B From the sketch we can see that x 0 L = A 0 and xl = A Emf = A A 0 B = BA BA 0 Emf = Φ Φ 0 = Φ t The induced emf equals the time rate of change of the magnetic flux If there are N number of coils, emf = N Φ BA=Φ t This is almost always written as emf =  N Φ t
4 EMF =  N Φ t The direction of the induced current is such that the magnitude of force F acts on the rod to oppose its motion, slowing the rod down The minus sign is a reminder that the induced current creates a magnetic field that opposes the force This is Faradays Law of electromagnetic induction Φ = change in magnetic flux through 1 loop t = time interval during which change occurs Φ t = average time rate of change of flux that passes though one loop
5 EXAMPLE A coil of wire consists of 20 turns or loops, each of which has an area of m 2. A magnetic field is perpendicular to the surface of each loop at all times, so that θ = θ 0 = 0 0. At time t 0 = 0s, the magnitude of the field at a location of the coil is B 0 = 0.050T. At a later time t = 0.10s, the magnitude of the field at the coil has increased to B = 0.060T. Find the average emf induced in the coil during this time. emf = N Φ Φ 0 = N BAcos θ BA o cos θ = NA cos θ B B 0 emf = cos = V
6 DIRECTION OF THE INDUCED CURRENT Lenz law: The direction of the induced current creates an induced magnetic field that opposes the motion of the inducing field Move N pole towards coil Oppose wants to repel creates N pole Find direction of current using RHR2 Move N pole away from coil Oppose wants to attract creates a S pole Find direction of current using RHR2
7 Lenz s Law Changing the area of a coil in a constant magnetic field induces a current Magnetic flux will change if the area of the loop changes: If the area is decreased, the current tries to maintain the original flux by producing its own magnetic field into the page, so increasing flux
8 LENZ LAW CONTINUED An induced emf drives a current around a circuit just as a battery Conventional current from + to terminal The net magnetic field penetrating a coil of wire results from 2 combinations: Original magnetic field that produces changing flux, leads to an induced emf Induced current creates its own magnetic field, which is called induced magnetic field
9 LENZ LAW The induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change
10 REASONING STRATEGY 1. Determine whether the magnetic flux that is penetrating a coil is increasing or decreasing 2. Find what direction of induced magnetic field must be so that it can oppose the change in magnetic flux by adding or subtracting from the original field 3. Finding direction of induced magnetic field then use RHR2 to find direction of induced current A current will be induced In such a way that its Magnetic flux will oppose The incoming magnet
11 SOLENOIDS AND STRAIGHT CONDUCTORS The induction of polarity is in accordance with the Law of energy conservation If this solenoid would have an induced S pole:  Magnet would accelerate towards it because of attraction  More induced current produced creating more acceleration KE would increase indefinitely  Energy would be created  Impossible  Induced current must oppose the change producing it
12 PROBLEM SOLVING STEPS Is the magnetic flux inside a loop increasing, decreasing or unchanged? S v N Flux is increasing Loop wants to oppose change Induces magnetic field that is opposing increase By RHR2: current is up or ccw Flux from magnet Flux from induced current Current ccw
13 CONTINUED v Flux inside loop is decreasing Loop wants to oppose change Creates magnetic field is same direction as bar magnetic field, so increasing flux By RHR current is down or cw Current is cw
14 SUMMARY The magnetic field of induced current in a loop: If flux is increasing: induced magnetic field points opposite direction as external field to decrease total flux If flux is decreasing induced magnetic field points in same direction as external field to increase total flux Use the right hand rule to find the current that produces the required flux density
15 FALLING THROUGH A MAGNETIC FIELD The induced field is not always opposite the external field because Lenz s law requires only that it must oppose the change in the flux that generates the emf A copper ring passes through a rectangular region with a constant magnetic field into the page. Describe the flux changes at each stage
16 COPPER RING A. no current because no change in flux B. Flux increases  induced field opposes change  wants to decrease field  field must point out of page  current must be ccw C. No change in flux no current D. Flux decreases  induced field wants to increase flux  field must point in same direction as external field or into the page  current must be cw E. No change in flux no current
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