# Electromagnetic Induction

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Electromagnetic Induction
Objective: TSW understand and apply the concept of magnetic flux in order to explain how induced emfs are created and calculate their value and polarity.

Chapter 20 Homework Problems: 4, 9, 15, 17, 19, 22, 23
You will be responsible for the content contained in chapter 20, sections 1&2 of the textbook. Take the time to read these sections. Chapter 20 Homework Problems: 4, 9, 15, 17, 19, 22, 23

Electromagnetic induction is the process by which an emf (voltage) is produced in a wire by a changing magnetic flux. Magnetic flux is the product of the magnetic field and the area through which the magnetic field passes. Electromagnetic induction is the principle behind the electric generator. The direction of the induced current due to the induced emf is governed by Lenz’s Law.

Here is a visual model of what we did in chapter 19:
Loop of wire and an External magnetic field Output Force (wire moves) Input Current Electric Motor

Here is a visual model of what we will do in chapter 20:
Loop of wire and an External magnetic field Input Force (move wire) Output Current Generator

The next two slides contain vocabulary and equations, you should commit them to memory

Important Terms alternating current - electric current that rapidly reverses its direction electric generator - a device that uses electromagnetic induction to convert mechanical energy into electrical energy electromagnetic induction - inducing a voltage in a conductor by changing the magnetic field around the conductor induced current - the current produced by electromagnetic induction induced emf - the voltage produced by electromagnetic induction Faraday’s law of induction - law which states that a voltage can be induced in a conductor by changing the magnetic field around the conductor Lenz’s law - the induced emf or current in a wire produces a magnetic flux which opposes the change in flux that produced it by electromagnetic induction magnetic flux - the product of the magnetic field and the area through which the magnetic field lines pass. motional emf - emf or voltage induced in a wire due to relative motion between the wire and a magnetic field

Equations, Symbols, and Units
where ε = emf (voltage) induced by electromagnetic induction (V) v = relative speed between a conductor and a magnetic field (m/s) B = magnetic field (T) L = length of a conductor in a magnetic field (m) I = current (A) R = resistance (Ω) Φ = magnetic flux (Tm2 = Weber=Wb) A = area through which the flux is passing (m2) = angle between the direction of the magnetic field and the area through which it passes

Magnetic Flux Consider a rectangular loop of wire of height L and width x which sits in a region of magnetic field of strength B. The magnetic field is directed into the page, as shown below: L w The magnetic flux is given by the following equation: Φ = The magnetic flux (Tm2 = Wb) B = The magnetic field (T) A = area of loop (m2) Φ = angle between the field and the area

Faraday’s law states that an induced emf is produced by changing the flux, but how could the flux be changed? Turn the field off or on. Move the loop of wire out of the field Rotate the loop to change the angle between the field and the area of the loop.

Here is Faraday’s Law in equation form:
Where Є = The induced emf (voltage) (V) ΔΦ = The change in flux (Wb) Δt = The change in time (s) N = number of loops. *Note that an emf is only produced if the flux changes. The quicker the flux changes the larger the induced emf.

The induced emf in the wire will produce a current in the wire
The induced emf in the wire will produce a current in the wire. The magnitude of the induced current is found using Ohm’s Law:

It is helpful to use RHR#2 when using Lenz’s Law.
The direction of the induced current is found using Lenz’s Law (conservation of energy). Lenz’s Law – The induced current in a wire produces a magnetic field such the flux of the produced magnetic field opposes the original change in flux. In simple terms the wire resists the change in flux and wants to go back to the way things were. It is helpful to use RHR#2 when using Lenz’s Law.

Example 1: A circular loop of wire with a resistance of 0
Example 1: A circular loop of wire with a resistance of 0.5Ω and radius 30cm is placed in an external magnetic field of 0.2T. The magnetic field is turned off in .02 seconds. Calculate the original flux of the loop. Calculate the induced emf. Calculate the current induced in the wire. What direction does the induced current have? What other way could the same emf be induced without turning the field off? • • • •

Let’s do some examples predicting the induced current direction using Lenz’s Law

• • • • • • • • X X X X X X X X Bout decreasing flux
• • • • • • • • Bout decreasing flux Bout increasing flux CCW CW X X X X X X X X Bin decreasing flux Bin increasing flux CCW CW

If you are really struggling applying Lenz’s Law, then memorize the following table:
decreasing Increasing B out CCW CW B in

Calculate the induced emf in the circuit.
Example 2: A circuit with a total resistance of 5Ω is made using a set of metal wires and a copper bar. The magnetic field is directed into the page as shown in the diagram. The bar starts on the left and is pulled to the right at a constant velocity. Calculate the induced emf in the circuit. Calculate the current induced in the wire. What direction does the induced current have? What is the magnitude and direction of the magnetic force that opposes the motion of the bar? X X X X X X X v L

The last example led to the equation for the motional emf
The last example led to the equation for the motional emf. The motional emf is the voltage induced in a wire as it moves in an external magnetic field. The induced emf will produce a current in the wire, which will in turn result in a force that opposes the motion of the wire. You don’t get something for nothing. Motional emf Where Є = The induced emf (V) B = The external magnetic field (T) L = The length of the wire (m) v = The velocity of the wire (m/s)

Find the emf induced in the rod.
Example 3: A conducting rod of length 0.30 m and resistance 10.0 Ω moves with a speed of 2.0 m/s through a magnetic field of 0.20 T which is directed out of the page. v B (out of the page) L Find the emf induced in the rod. Find the current in the rod and the direction it flows. Find the power dissipated in the rod. d) Find the magnetic force opposing the motion of the rod.

Example 4: A square loop of sides a = 0. 4 m, mass m = 1
Example 4: A square loop of sides a = 0.4 m, mass m = 1.5 kg, and resistance 5.0 Ω falls from rest from a height h = 1.0 m toward a uniform magnetic field B which is directed into the page as shown. Determine the speed of the loop just before it enters the magnetic field. As the loop enters the magnetic field, an emf ε and a current I is induced in the loop. (b) Is the direction of the induced current in the loop clockwise or counterclockwise? Briefly explain how you arrived at your answer. When the loop enters the magnetic field, it falls through with a constant velocity. (c) Calculate the magnetic force necessary to keep the loop falling at a constant velocity. (d) What is the magnitude of the magnetic field B necessary to keep the loop falling at a constant velocity? (e) Calculate the induced emf in the loop as it enters and exits the magnetic field. a B h

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