Chapter 23 Magnetic Flux and Faraday s Law of Induction

Chapter 23 Magnetic Flux and Faraday s Law of Induction

Units of Chapter 23 Induced Electromotive Force Magnetic Flux Faraday s Law of Induction Lenz s Law Mechanical Work and Electrical Energy Generators and Motors

Lenz s Law Lenz s Law An induced current always flows in a direction that opposes the change that caused it. Therefore, if the magnetic field is increasing, the magnetic field created by the induced current will be in the opposite direction; if decreasing, it will be in the same direction.

Motional emf: Qualitative This conducting rod completes the circuit. As it falls, the magnetic flux decreases, and a current is induced.

Motional emf: Qualitative The force due to the induced current is upward, slowing the fall. Since an emf is produced in the system, it is referred to as motional emf.

Mechanical Work and Electrical Energy Motional emf: Quantitative This diagram shows the variables we need to calculate to calculate the induced emf. A rod is pushed by an external force, so it moves to the right with constant speed v.

Motional emf: Quantitative 1) Calculate the change in flux: 2) Using Faraday s law calculate the magnitude of the induced emf. 3) Electric field caused by the motion of the rod

Change in flux: Induced emf: Motional emf: Quantitative Electric field caused by the motion of the rod: EUREKA A CHANGING MAGNETIC FLUX DOES INDEED CREATE AN ELECTRIC FIELD. Only one resistance, the current is: I B R in v

Consider the setup shown in the figure. What can cause the bar to move with velocity v: A. Evil physics professor B. Applied force on bar pulling to right C. Applied force on bar pulling to left D. Magnetic forces 10/30/2013 9

Consider the setup shown in the figure where current I is flowing through the mobile bar. What is the effect of the magnetic force acting on the bar? I A. It is too small to have an effect. B. It has an effect in the same direction as the applied force. C. It has an effect in the opposite direction as the applied force. 10/30/2013 10

Mechanical Work and Electrical Energy If the rod is to move at a constant speed, an external force must be exerted on it. This force should have equal magnitude and opposite direction to the magnetic force. 1) Calculate the magnetic force:

Mechanical Work and Electrical Energy 2) Calculate mechanical power delivered by the external force: 3) Compare this to the electrical power in the light bulb: EUREKA, mechanical power has been converted directly into electrical power.

PROBLEM: Lighting a bulb The graph below shows a circuit consisting of a flashlight bulb, rated 3.0V/1.5 W, and ideal wires with no resistance. The right wire of the circuit, which is 10 cm long, is pulled at constant speed v through a perpendicular magnetic field of strength 0.10 T. a. What speed must the wire have to light the bulb to full brightness? b. What force is needed to keep the wire moving? 13 10/30/2013

Work it at home: wire in the magnetic field Over a region where the vertical component of the Earth's magnetic field is 40.0µT directed downward, a 5.00 m length of wire is held in an east-west direction and moved horizontally to the north with a speed of 10.0 m/s. Calculate the potential difference between the ends of the wire, and determine which end is positive. Also, work out all the examples and active examples from the book 14 10/30/2013

Generators and Motors An electric generator converts mechanical energy into electric energy: An outside source of energy is used to turn the coil, thereby generating electricity.

Generators and Motors The induced emf in a rotating coil varies sinusoidally: The induced emf in the coil alternates in sign, which means that the current in the coil alternates in direction alternating-current generator, ac generator.

Torque on a current-carrying wire in a magnetic field. Recall that a generator has a current-carrying coil in a magnetic field. A. No problem that was in Chap. 29 and no longer relevant. B. Generator coil will experience a torque which makes the coil spin faster. C. Generator coil will experience a torque which makes the coil spin slower. 10/30/2013 17

Electric generators and motors Hybrid vehicles are designed so that their electric motors are equipped with circuits to take advantage of regenerative braking, effectively converting the motor to a generator to recharge the batteries when the breaks are activated. Other uses for inductors Rechargeable electric toothbrush Induction heating cooking 10/30/2013 18

Uses of Faraday s law continued: http://theinductionsite.com/how-induction-works.shtml 10/30/2013 PHY 114 A Spring 2012 -- Lecture 13 19

Motors An electric motor is exactly the opposite of a generator it uses the torque on a current loop to create mechanical energy.

Inductance When the switch is closed in this circuit, a current is established that increases with time.

23-7 Inductance Inductance is the proportionality constant that tells us how much emf will be induced for a given rate of change in current: Solving for L,

Inductance Given the definition of inductance, the inductance of a solenoid can be calculated: When used in a circuit, such a solenoid (or other coil) is called an inductor.

Home Example: solenoid A solenoid of radius 2.5cm has 400 turns and a length of 20 cm. Find (a) its inductance and (b) the rate at which current must change through it to produce an emf of 75mV. 24 10/30/2013

RL Circuits R is resistor and L inductor. When the switch is closed, the current immediately starts to increase. The back emf in the inductor is large, as the current is changing rapidly. As time goes on, the current increases more slowly, and the potential difference across the inductor decreases.

RL Circuits This shows the current in an RL circuit as a function of time. The characteristic time is:

The LR circuit reminds us of: A. Why physics class is so beautiful. B. Why physics class is so terrible. C. RC circuit. D. Money in the bank. 10/30/2013 27

Energy Stored in a Magnetic Field It takes energy to establish a current in an inductor; this energy is stored in the inductor s magnetic field. Considering the emf needed to establish a particular current, and the power involved, we find:

Energy Stored in a Magnetic Field We know the inductance of a solenoid; therefore, the magnetic energy stored in a solenoid is: Dividing by the volume to find the energy density gives: This result is valid for any magnetic field, regardless of source.

Transformers A transformer is used to change voltage in an alternating current from one value to another.

Transformers By applying Faraday s law of induction to both coils, we find: Here, p stands for the primary coil and s the secondary.

Transformers The power in both circuits must be the same; therefore, if the voltage is lower, the current must be higher.

Summary of Chapter 23 A changing magnetic field can induce a current in a circuit. The magnitude of the induced current depends on the rate of change of the magnetic field. Magnetic flux: Faraday s law gives the induced emf:

Summary of Chapter 23 Lenz s law: an induced current flows in the direction that opposes the change that created the current. Motional emf: emf produced by a generator: An electric motor is basically a generator operated in reverse. Inductance occurs when a coil with a changing current induces an emf in itself.

Summary of Chapter 23 Definition of inductance: Inductance of a solenoid: An RL circuit has a characteristic time constant:

Summary of Chapter 23 Current in an RL circuit after closing the switch: Magnetic energy density: Transformer equation: