Chp' 31 Induction and Inductance slide 1

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• Chapter 31
• Induction and Inductance
• AIMS
• Faradays law of induction (em)
• B-fields ? electric fields
• Lenzs law
• Motional emf
• Induced electric fields
• Inductors
• self-induction
• mutual induction
• RL circuits
• Energy stored in B-fields

Chapter 30 electric current ? B-fields
What is an electromotive force (emf)? Source of
energy ie. An ordinary battery that provides a
potential difference between two points in a
circuit. Other examples solar cell, fuel
cells, human heart

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31-3 Faradays law of Induction
Law of induction 1831 (Faraday -
England) (Henry - USA)
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Sample problem 31-1 - important
Checkpoint 1
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31-4 Lenzs Law
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Sample problems 31-2 and 31-3 - important
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31-5 Induction and Energy transfers Motional emf
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Motional emf cont.
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Sample problem 31-4 (a) Plot the flux through the
loop as a function of x (b) Plot the induced emf
as a function of position of the loop, indicate
the directions of the induced emf (c) Plot the
rate of production of thermal energy in the loop
as a function of the position of the loop.
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(b) Plot the induced emf as a function of
position of the loop, indicate the directions of
the induced emf
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(c) Plot the rate of production of thermal energy
in the loop as a function of the position of the
loop.

• Checkpoint 3
• maximum magnitude of emf
• side which intersects the B-field

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31-7 Inductors and Inductance Inductance
Faradays law implies that a changing magnetic
flux through a circuit produces an induced emf in
the circuit. In the special case when that
changing flux is itself caused by a changing
current in an electric circuit, we speak of the
inductance of the circuit.
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Inductance - Solenoid (ideal)
Magnetic flux linkage N?
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31-9 RL Circuit
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31-10 Energy stored in a magnetic field
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Chapter 31, Tutorial 3  
2E. A small loop of area A is inside of, and has
its axis in the same direction as, a long
solenoid of n turns per unit length and current
i. If i i0 sin wt, find the emf in the
loop.   Solution 14P. An elastic conducting
material is stretched into a circular loop of
12.0 cm radius. It is placed with its plane
perpendicular to a uniform 0.800 T magnetic
field. When released, the radius of the loop
starts to shrink at an instantaneous rate of 75.0
cm/s. What emf is induced in the loop at that
instant?   Solution   31E. A loop antenna
of area A and resistance R is perpendicular to a
uniform magnetic field B. The field drops
linearly to zero in a time interval of ?t. Find
and expression for the total thermal energy
dissipated in the loop.   Solution  
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33E. A metal rod is forced to move with constant
velocity v along two parallel metal rails,
connected with a strip of metal at one end, as
shown in figure 1. A magnetic field B 0.350 T
points out of the page. (a) If the rails are
separated by 25.0 cm and the speed of the rod is
55.0 cm/s, what emf is generated? (b) If the rod
has a resistance of 18.0 ?, and the rails and
connector have negligible resistance, what is the
current in the rod? (c) At what rate is energy
being transferred to thermal energy? Solutio
n (a) The flux changes because the area bounded
by the rod and rails increases as the rod moves.
Suppose that at some instance the rod is a
distance x from the right hand end of the rails
and has speed v. Then the flux through the area
is ?B BA BLx, where L is the distance between
the rails. According to Faradays law the
magnitude of the emf induced is ? d?B /dt
BL(dx/dt) BLv (0.350 T)(0.250 m)(0.550 m/s)
4.81x10-2 V.   (b) Use Ohms law. If R is the
resistance of the rod then the current in the rod
is I ?/R (4.81x10-2 V)/(18.0 ?) 2.67x10-3
A.   (c) The rate at which thermal energy is
generated is
Figure 1
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36P. Two straight conducting rails form a right
angle where their ends are joined. A conducting
bar in contact with the rails starts at the
vertex at time t 0 and moves with constant
velocity of 5.20 m/s along them, as shown in
figure 2. A 0.350 T magnetic field points out of
the page. Calculate (a) the flux through the
triangle formed by the rails and the bar at t
3.00 s and (b) the emf around the triangle at
that time. (c) If we write the emf as ? atn,
where a and n are constants, what is the value of
n?
Figure 2
             Solution (a)At time t the area of
the closed triangle loop is A(t) ½(vt)(2vt)
v2t2. Thus   (b)   (c) From part (b)
above we see that ? ?2Bv2t ? t1. Thus n
1.
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