Magnetic Induction 1Physics is Life

Objectives To learn how magnetic fields can produce currents in conductors To understand how this effect is applied in the electrical generator to convert mechanical energy to electrical energy To learn how a changing current in one circuit induces an electromotive force in a nearby circuit. 2Physics is Life

Faraday’s Demonstration of Electromagnetic Induction Oersted discovered that every electric current produces a magnetic field. We now see that the reverse is true: A magnetic field can induce a current. The process whereby this is done is called electromagnetic induction. It was discovered by Michael Faraday ( ) in England. Such a current is said to be induced. 3Physics is Life

Faraday’s Demonstration of Electromagnetic Induction 4Physics is Life

Induced EMF To make a current flow in a circuit, there must be a source of energy or EMF (electromotive force). In a circuit containing a battery, the battery produces the EMF. In the circuits shown below, the movement of the wire (or the magnet) supplies the energy that moves the electrons through the circuit. 5Physics is Life

v B induced potential Induced EMF 6Physics is Life

Source of Induced EMF The EMF induced in a wire of length l that cuts across a magnetic field B at velocity v is EMF = vBL This relationship is one form of the law known as Farady’s law of induction. In SI units, v is expressed in meters per second, B is in webers per square meter and L is in meters, The EMF then comes out in volts. 7Physics is Life

Relative Motion and Induction It makes no difference whether the magnetic field moves past a stationary wire or the wire moves through a stationary magnetic field. Only the relative velocity between the wire and magnetic field is necessary to induce EMF. In both cases, the EMF is equal to vBL 8Physics is Life

Source of Induced EMF Sample Problem A wire 0.4m long moves across a uniform magnetic field in which the induction is 2 x Wb/m 2 at the velocity of 5 m/s. (a) What EMF is induced in the wire. (b) If the wire is in a circuit of resistance 0.2 , what current flows through it? (c) What force must be applied to the wire to keep it moving through the magnetic field? (a) EMF =vBL = (5m/s)(2 x Wb/m 2 )(0.4m) = 0.04V (b) I = V/R = 0.04V/ 0.2  = 0.2A (c) F=ILB = (0.2A)(0.4m)(2 x Wb/m 2 ) = 2 x N 9Physics is Life

Source of Induced EMF Sample Problem At what speed (v) must a 0.20m length of wire cut across a magnetic field for which B is 2.5 Wb/m 2 to have an EMF of 10V induced in it? v = EMF/BL = 10V/[(2.5Wb/m2)(0.20)] = 20 m/s 10Physics is Life

Factors Affecting the Induced EMF From the law of induction, it appears that the EMF induced in a wire conductor moving across the lines of force of a magnetic field may be increased in three ways: Increasing the velocity v with which the wire is moving Increasing the magnetic field B Increasing the length l of the wire cutting across the magnetic lines of force 11Physics is Life

Direction of Induced Current The direction of the induced current is readily found by following the following rule: If the right hand is held so that the middle finger points in the direction of the magnetic field and the index finger points in the direction of the moving wire, the extended thumb will point in the direction of the induced current. 12Physics is Life

Alternating Current Generator A generator is the opposite of a motor – it transforms mechanical energy into electrical energy. This is an ac generator: The axle is rotated by an external force such as falling water or steam. The brushes are in constant electrical contact with the slip rings. How does a generator differ from a motor? 13Physics is Life

Generator and Motor Compared The construction is the same. They only differ in use. In the generator, mechanical energy is supplied to rotate the armature and is converted into electrical energy. In the motor, the process is reversed. Electrical energy is supplied to rotate the armature and is converted into mechanical energy. Thus a generator can be used as a motor and a motor can be used as a generator. 14Physics is Life

15 So far, we have expressed the EMF induced in a circuit in terms of the rate at which a moving conductor that is part of the circuit cuts across magnetic field lines of force. Another useful way to express the EMF produced in a circuit is in terms of the rate at which the number of lines of force or magnetic flux (  B ) passing through the entire circuit changes. Changing Magnetic Flux and Induced EMF

Faraday investigated quantitatively what factors influence the magnitude of the EMF induced. He found first of all that it depends on time: the more rapidly the magnetic field changes, the greater the induced EMF. But the EMF is not simply proportional to the rate change of the magnetic field B. Rather it is proportional to the rate of change of the magnetic flux,  B, passing through the loop of area A, which is defined as:  B = BAcos  If the flux through N loops of wire changes by an amount  B during a time  t, the average induced EMF during this time is EMF = -N  B /  t This is known as Faraday’s Law of Induction 16Physics is Life

Changing Magnetic Flux and Induced EMF The minus sign is placed there to remind us in which direction the induced EMF acts. Experiments show that the induced EMF always gives rise to a current whose magnetic field opposes the original change in flux (Lenz’s Law). Now we have two ways to calculate EMF: 17Physics is Life This is a diagram that shows the induced current for moving negative charges (Left hand!) EMF (  ) = vBL= -N  B /  t where  B = BA 2 –BA 1 Now let’s take a look at all of the factors that affect magnetic flux:

Physics is Life18 1. By changing the orientation of the loop in the field. If the field passes through the flat side of the loop, the flux is greater than if the field lines lie parallel to the side of the loop (cos  ) 2. By changing the area of the loop. More area allows more magnetic field to be directed through the loop 3. By varying the magnetic field strength. This can be done in many ways; one way is to draw a bar magnet closer or further away from the loop Flux can be thought of as the amount of magnetic field (represented in the diagrams below by green arrows) directed through the loop. Flux (  B =BAcos  ) can be varied in the following three ways: Faraday’s Law of Induction: Magnetic Flux

Physics is Life19 Lets take a closer look at the angle that the loop makes with the magnetic field: Faraday’s Law of Induction: Magnetic Flux Note: The angle  is the angle between the magnetic field and the normal to the plane of the loop, not the angle between the magnetic field and the plane of the loop Now that we understand the factors that magnetic flux. Let us investigate the direction of the induced current when there is a change in magnetic flux

Lenz’s Law Let us apply Lenz’s law to the experiment shown. When the north pole of the magnet moves toward the front end of the coil, the current induced in the coil sets up a magnetic field that opposes that motion. To do this, the induced current flows in such a direction as to produce a magnetic north pole in front of the coil that repels the north pole of the approaching magnet. 20Physics is Life

Lenz’s Law When the north pole of the magnet is withdrawn from the coil, the induced current reverses direction and sets up a magnetic south pole at the front end of the coil. The south pole of the coil attracts the north pole of the magnet thus opposing its movement away from the coil 21Physics is Life

22 Faraday’s Law of Induction; Lenz’s Law Sample problem The magnetic induction through a rectangular loop of wire 0.2m long by 0.1m wide increases from 0 to 0.4T in s. What EMF is produced in the loop? Area= (0.2m)(0.1 m) =.02m 2 The change in magnetic flux (  B ) = -BA = -0.4 T x 0.02m 2 = Tm 2 EMF (  ) = -BA/  t = 0.008Tm 2 /10 -3 s = 8 V EMF (  ) = vBL= -N  B /  t where  B = BA 2 –BA 1

Physics is Life23 Changing Magnetic Flux Produces an Electric Field A changing magnetic flux induces an electric field; this is a generalization of Faraday’s law. The electric field will exist regardless of whether there are any conductors around. E = F/q = qvB/q = vB

Physics is Life24 Changing Magnetic Flux Produces an Electric Field Sample Problem Electrons moving at 3.6 x 10 4 m/s pass through an electric field with an intensity of 5.8 x 10 3 N/C. How large a magnetic field must the electrons also experience for their path to be undeflected? E = vB, so B = E/v = 0.16T

Physics is Life25 Summary Magnetic flux: Changing magnetic flux induces emf: Induced emf produces current that opposes original flux change Changing magnetic field produces an electric field Electric generator changes mechanical energy to electrical energy; electric motor does the opposite A changing magnetic flux induces an electric field; this is a generalization of Faraday’s law. The electric field will exist regardless of whether there are any conductors around. E = F/q = qvB/q = vB