Chapter 20: Electromagnetic Induction 20.1:Induced Emf’s: Faraday’s Law and Lenz’s Law 20.2-4: Omitted Homework for Chapter 20 Read Chapter 20 HW 20: p.658-660: 3,5,6,8,9,10,11,13,14,18,21-24.
20.1 Induced Emf’s : Faraday’s Law and Lenz’s Law
It is more like an electromagnet, because the movements of the metal liquids create electrical currents which change in strength and direction.
When there is no relative motion between the magnet and the loop, the number of field lines (in the diagram, 7) through the loop is constant. The galvanometer (measuring current) shows no deflection. electromagnetic induction - The process of generating a current through a circuit due to the relative motion between a wire and a magnetic field when the wire is moved through the magnetic field or the magnetic field moves past the wire. As we saw in Chapter 19, electric current produces a magnetic field. On the flip side, changing magnetic fields can be used to produce electric current.
Moving the magnet away from the loop decreases the number of field lines passing through the loop (now 5). The induced current is in the opposite direction as indicated by the opposite needle deflection. Moving the magnet toward the loop increases the number of field lines now passing through the loop (now 12). An induced current is detected by the galvanometer.
The induced current can also occur if the loop is moved toward or away from a stationary magnet. The magnitude of the induced current depends on the speed of that relative motion. Exception: When a loop is moved parallel to a uniform magnetic field, there is no change in the number of field lines passing through the loop and no induced current.
Another way to induce a current in a stationary loop of wire is to vary the current in another loop close to it. When the switch is closing in the right-loop circuit, the current buildup (typically over a few milliseconds) produces a changing magnetic field that passes through the other loop, inducing a current in it. When the switch is opened the magnetic field lines through the left- hand loop decreases. The induced current in this loop is then in the opposite direction.
The current induced in a loop is caused by an induced electromotive force (emf) due to electromagnetic induction. An emf represents energy capable of moving charges around a circuit. We previously studied batteries as a chemical source of emf. A moving magnet can create an induced emf in a stationary loop, which causes current. In the case of two stationary loops, where a changing current in one circuit induces an emf in the other, we call it mutual induction..
Micheal Faraday (1791-1867) Micheal Faraday and Joseph Henry conducted independent experiments on electromagnetic induction around 1830. Faraday drew the conclusion: An induced emf is produced in a loop by changing the number of magnetic field lines passing through the plane of the loop.
magnetic flux ( ) – a measure of the number of field lines passing through and area (A). The variable we use to represent magnetic flux is capital phi. a)The area can be represented by a vector A perpendicular to the plane of the area. b) When the plane of a rotating loop is perpendicular to the field and = 0°, then = max = BA. c) When = 180°, the magnetic flux has the same magnitude but is opposite in direction: = - max = - BA. d) When and = 90°, then = 0. e) As the loop is rotated from an orientation perpendicular to the field to one more nearly parallel to the field, less area is open to the field lines and the flux decreases. In general, = BA cos . Side View
m = BA cos magnetic flux whereB is the magnetic field A is the area of the loop is the angle between B and A The unit of magnetic flux is the weber (Wb). 1 Wb = 1 T·m 2 If the coil has N number of turns, then the total flux through the coil is the sum of the flux through each turn. Hence, m = NBA cos magnetic flux through a solenoid On Gold Sheet
Example 20.1: A circular loop of radius 0.20 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are (a) parallel, (b) perpendicular, (c) at 60°.
Examples: pacemakers stopping, migrating birds get lost, GPS won’t work, etc.
For N loops of wire, Faraday’s Law of Induction can be written: = - N m t (average for the time interval t)
In other words, Lenz’s Law states that the direction of the induced current opposes the increase in flux.
Example 20.2: A coil is wrapped with 100 turns of wire on a square frame with sides 18 cm. A magnetic field is applied perpendicular to the plane of the coil. If the field changes uniformly from 0 to 0.50 T in 8.0 s, find the average value of the magnitude of the induced emf.
Example 20.3: A square coil of wire with 15 turns and an area of 0.40 m 2 is placed parallel to a magnetic field of 0.75 T. The coil is flipped so its plane is perpendicular to the magnetic field in 0.050 s. What is the magnitude of the average induced emf?
Example 20.4: An airplane with a wing span of 50 m flies horizontally with a speed of 200 m/s above the Earth at a location where the downward component of the Earth’s magnetic field is 6.0 x 10 -5 T. Find the magnitude of the induced emf between the tips of the wing.
Check for Understanding 1.The unit of magnetic flux is a) Wb b) T·m 2 c) T·m / A d) both a and b Answer: d 2. Magnetic flux through a loop can change due to a change in a) the area of the coil b) the magnetic field strength c) the orientation of the loop d) all of the above Answer: d
Check for Understanding 3.For an induced current to appear in a loop of wire, a) there must be a large magnetic flux through the loop b) the loop must be parallel to the magnetic field c) the loop must be perpendicular to the magnetic field d) the magnetic flux through the loop must vary with time Answer: d
Chapter 20 Formulas m = NBA cos magnetic flux N is the number of loops B is the magnetic field A is the area of the loop is the angle between B and A = - N m averageinduced emf tN is the number of loops m is the final minus initial magnetic flux t is the final minus initial time = BLvinduced motional emf B is the magnetic field L is the length of the conductor v is the speed of the conductor