INDUCED VOLTAGES AND
INDUCTANCE
A Summary from College Physics by Raymond.
Serway
Induced Emf And Magnetic Flux
The magnetic flux ∅B through a closed loop is defined
as
where B is the strength of the uniform magnetic field,
A is the cross-sectional area of the loop, and θ is the
angle between B and a direction perpendicular to the
plane of the loop.
The value of the magnetic flux is proportional to
the total number of lines passing through the loop
Faraday’s experiment.
When the switch in the primary circuit at the left is
closed, the ammeter in the secondary circuit at the
right measures a momentary current.
Conclusion:
• The emf in the secondary circuit is induced by the
changing magnetic field through the coil in that
circuit.
• An electric current could be produced by a changing
magnetic field.
Faraday’s Law of Induction
Principle: a current is set up in the
circuit as long as there is relative motion
between the magnet and the loop.
Faraday’s
law
of
magnetic
induction: If a circuit contains N
tightly wound loops and the
magnetic flux through each loop
changes by the amount ∆∅B during
the interval ∆t, the average emf
induced in the circuit during time ∆t
is
Lenz’s law
Lenz’ Law describe the polarity of voltage: The current caused by the induced emf
travels in the direction that creates a magnetic field with flux opposing the change in
the original flux through the circuit.
If the magnetic flux through a loop is becoming more positive, say, then the induced
emf creates a current and associated magnetic field that produces negative magnetic
flux. An example of Lenz’s law.
Applications of EMF Induced
Electric Guitar:
Vibration of magnetized string at a frequencies → varies the
magnetic flux → changing the induced voltage → sent to
amplifier → loudspeaker
Applications of EMF Induced
Tape Recorder:
• A magnetic tape moves past a recording and playback head.
• The tape is a plastic ribbon coated with iron oxide or chromium
oxide.
Example process to record a sound:
• A sound wave sent into a microphone is transformed into an
electric current, amplified, and allowed to pass through a wire
coiled around a doughnut-shaped piece of iron, which functions
as the recording head.
• The iron ring and the wire constitute an electromagnet, in which
the lines of the magnetic field are contained completely inside
the iron except at the point where a slot is cut in the ring.
• Here the magnetic field fringes out of the iron and magnetizes
the small pieces of iron oxide embedded in the tape.
• As the tape moves past the slot, it becomes magnetized in a
pattern that reproduces both the frequency and the intensity of
the sound signal entering the microphone.
Applications of EMF Induced
AC Generator
An emf is induced in a coil, which rotates by some external
means in a magnetic field
Applications of EMF Induced
DC Generator
The emf fluctuates in magnitude, but always has the same
polarity. The output voltage always has the same polarity and
the current is a pulsating direct current
Self-inductance
What is the self-induction?
As the current increases with time towards its
equilibrium value → the magnetic flux through the loop
due to this current also increases→ induces an emf in the
circuit that opposes the change in magnetic flux.
By Lenz’s law, the induced emf is in the direction indicated by
the dashed battery in the figure. The net potential difference
across the resistor is the emf of the battery minus the opposing
induced emf.
As the magnitude of the current increases → the rate of
increase lessens and hence the induced emf decreases.
This opposing emf results in a gradual increase in the
current.
For the same reason, when the switch is opened, the current
doesn’t immediately fall to zero.
Self-inductance
The self-induced emf must be proportional to the rate of
change of the current with time
L is a proportionality constant called the inductance of the
device. The SI unit of inductance is the henry (H)
The negative sign indicates that a changing current induces
an emf in opposition to the change. This means that if the
current is increasing (∆I positive), the induced emf is
negative, indicating opposition to the increase in current,
VICE VERSA
RL Circuit
A circuit element that has a large inductance, such
as a closely wrapped coil of many turns, is called an inductor
1. at t = 0: The current begins to increase, but
the inductor produces an emf that opposes
the increasing current. As a result, the
current can’t change from zero to its
maximum value of ε/R instantaneously.
2. As the current approaches its steady-state
value, the back emf of the coil falls off
because the current is changing more
slowly.
3. Finally, when the current reaches its
steady-state value, the rate of change is
zero and the back emf is also zero.
Energy Stored In A Magnetic Field