Electric Potential

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Self Inductance
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Self Inductance
A variable power supply is connected to a loop.
The current in the loop creates a magnetic
field. What happens when the power supply dial
is turned down reducing the current, or turned up
increasing the current?
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Self Induction
R
The current does not go from zero to e/R in the
circuit immediately after the switch is closed
1. as the current flows through, magnetic flux
through the loop is set up
2. this is opposed by induced emf in the loop
which opposes the change in net magnetic
flux 3. by Lentzs law, the induced E-field
opposes the current flow
4
Self Induction
R
As a time-varying current flow through the
conductor, the same thing happens 1. as the
changing current flows through, the magnetic
flux through the loop changes 2. this is
opposed by induced emf in the loop which
opposes the change in net magnetic flux 3. by
Lentzs law, the induced E-field opposes the
current flow
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Self-Inductance in a closed loop
We must keep the shape and size of the loop fixed.
(From the Biot-Savart Law)
The self-inductance L is the proportionality
constant. It depends on the shape of the loop,
that is, its geometry.The self-induced ems is
proportional to the rate of change of the current
(definition of L)
Unit for L 1 henry (H) 1 (Vs)/A
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From Faradays Law for N loops and our
definition of inductance, L
An equivalent definition of L uses the integral
of the above where F is the flux through each
loop produced by current I in each loop
To find L we use
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Quiz
A flat circular coil with 10 turns (each loop
identical) has inductance L1 . A second coil, of
the same size, shape and current passing through
the conductor but with 20 turns, would have
inductance

1. 2 L1 B) ½ L1 C) 4 L1 D) ¼ L1
   E) L1

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Also
We can see that inductance is the measure of the
opposition to the change in current, I. (Recall
that resistance, R, is the opposition to
current, I RV/I)
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Example 1 Long solenoid
B
I
2r
I
l
Given N 300 turns r 1 cm l
25cm Calculate L
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Solution
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Example 2 Long solenoid
B
I
2r
I
l
Given N 300 turns r 1 cm l
25cmdI/dt -50 A/s Calculate the
self-induced emf
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Solution
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Example 3 Self-Inductance of a coaxial cable
b
a
I
r
In the gap (a lt r lt b)
Show that
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Solution
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Kirchhoffs Loop Rule (again)
Voltage change in going along path from left to
right

• resistor,
• capacitor,
• inductor,

I
q
q
I
Path direction same as current
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Example 4
What is the current 2 ms after the switch is
closed? Hint write down Kirchoffs loop rule and
solve the differential equation for I
12 V
20mH
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Energy
-
I
How much work is done by an external emf to
increase the current from 0 to Ifinal ?
eL - LdI/dt
Kirchoffs law gives(Recall, PVI)
Power supplied by external emf power absorbed
by inductor
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Power absorbed by inductor is
The total potential energy stored is
Find the potential energy of an inductor with
L400mH and a final current of 10A.
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Examples of Inductors