chapter 23 magnetic flux and faraday’s law of...
TRANSCRIPT
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Chapter 23
Magnetic Flux and Faraday’s Law of Induction
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Overview of Chapter 23
• Induced Electromotive Force • Magnetic Flux • Faraday’s Law of Induction • Lenz’s Law • Mechanical Work and Electrical Energy • Generators and Motors • Inductance • RL Circuits • Energy Stored in a Magnetic Field • Transformers
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23-1 Induced Electromotive Force
Faraday’s experiment: closing the switch in the primary circuit induces a current in the secondary circuit, but only while the current in the primary circuit is changing.
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23-1 Induced Electromotive Force• Current in the secondary circuit is
0 if current in the primary circuit is not changing. !
• Current flows in the secondary circuit when current in the primary is changing. !
• Flows in opposite direction depending on whether the magnetic field is increasing or decreasing. !
• Magnitude of induced current proportional to rate at which the magnetic field is changing….
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23-1 Induced Electromotive Force
Note the motion of the magnet in each image
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23-2 Magnetic Flux
Magnetic flux is used in the calculation of the induced emf.
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23-3 Faraday’s Law of InductionFaraday’s law: An emf is induced only when the magnetic flux through a loop changes with time.
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23-3 Faraday’s Law of InductionMany devices that operate on the basis of Faraday’s law.
An electric guitar pickup:
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23-4 Lenz’s Law
Lenz’s Law
• Induced current always flows in a direction that opposes the change that caused it.
• If magnetic field is increasing (or decreasing), the magnetic field created by the induced current will be the opposite direction…
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23-4 Lenz’s Law
• This conducting rod completes the circuit. !
• As it falls, the magnetic flux decreases, and a current is induced.
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23-4 Lenz’s Law
The force due to the induced current is upward, slowing the fall.
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23-4 Lenz’s Law
Currents can also flow in bulk conductors. These induced currents, called eddy currents, can be powerful brakes.
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23-5 Mechanical Work and Electrical Energy
This diagram shows the variables we need to calculate the induced emf.
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23-5 Mechanical Work and Electrical Energy
Change in flux: Induced emf:
Electric field caused by the motion of the rod:
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23-5 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:
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23-5 Mechanical Work and Electrical Energy
Mechanical power delivered by the external force is:
Compare this to the electrical power in the light bulb:
Therefore, mechanical power has been converted directly into electrical power.
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23-6 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.
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23-6 Generators and Motors
The induced emf in a rotating coil varies sinusoidally:
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23-6 Generators and MotorsAn electric motor is exactly the opposite of a generator – it uses the torque on a current loop to create mechanical energy.
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23-7 Inductance
When the switch is closed in this circuit, a current is established that increases with time.
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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,
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23-7 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.
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23-8 RL Circuits
• Switch is closed, the current immediately starts to increase. • 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.
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23-8 RL CircuitsThis shows the current in an RL circuit as a function of time. The time constant is:
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23-9 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:
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23-9 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:
Result is valid for any magnetic field, regardless of source.
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23-10 TransformersA transformer is used to change voltage in an alternating current from one value to another.
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23-10 Transformers
By applying Faraday’s law of induction to both coils, we find:
Here, p stands for the primary coil and s the secondary.
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23-10 Transformers
The power in both circuits must be the same; therefore, if the voltage is lower, the current must be higher.
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Answer: 1.6 x 10-4 Wb
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Answer: 1.9 Wb
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Answer: 14 V
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Answer: 3.8 x 103
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Answer: 32.58 mT
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Answer: 15.5 mV
L = 353.2 µH
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Answer: a) 9.95 x 108 J/m3
Answer: b) 1.5 x 1010 V/m