Concept 26.1: The current induced in a
conductor by a change in magnetic flux acts to
create a magnetic flux that acts to oppose the
original change in magnetic flux.
26. Lenz’s Law
ε =−
• the minus sign in Faraday’s Law
• electric fields due to Faraday’s Law
This minus sign is
Lenz’s Law.
Serway and Beichner
Section 31.3, 31.4
Physics 1E03 Lecture 26
d
ΦB
dt
1
Bexternal
I
N
If there was no minus
sign, the induced
current would add to
the change in B,
making ε and I bigger.
The current would
grow without limit.
move
magnet
S
Physics 1E03 Lecture 26
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Bexternal
I
r
B ext increasing
Induced current creates a
field in opposite direction.
Physics 1E03 Lecture 26
3
r
B ext decreasing
Induced current creates a
field in the same direction
(inside the loop).
Physics 1E03 Lecture 26
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1
Quiz of concept 26.1
A magnet is dropped down the centre of a
long aluminum tube of radius R, and it is
found that it falls much more slowly than
if dropped outside the tube. The force on
the magnet that counteracts gravity is
due to the magnetic field created by
currents induced in the conducting tube.
The direction of the currents (as viewed
from above) is
A copper ring is held lightly just above
a solenoid. At time t=0 the switch
on the winding is closed so that a
current can flow through it. As a V
result the copper ring
a)
b)
c)
d)
flies upward
is pulled down
feels no net force
experiences a torque which twists
it sideways.
a)
b)
c)
d)
Physics 1E03 Lecture 26
A magnet (a magnetic dipole) is dropped down
the centre of a long aluminum tube of radius
R. The emf created in the tube depends on
the velocity of the magnet as
v
Physics 1E03 Lecture 26
Quiz of concept 26.1
v
6
2R
A magnet (a magnetic dipole) is dropped down
the centre of a long aluminum tube of radius
R. The resistance of the tube to the flow of
the induced current depends on the R as
S
N
S
N
v
b) v
d) 1/v
a) 1/R
c) 1/R3
Physics 1E03 Lecture 26
S
N
CW above the magnet and CCW below it
CCW above the magnet and CW below it
CW
CCW
5
2R
Quiz of concept 26.1
a) v2
c) independent of v
2R
Quiz of concept 26.1
7
b) 1/R2
d) R
Physics 1E03 Lecture 26
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2
Quiz of concept 26.1
2R
A magnet (a magnetic dipole) is dropped down
the centre of a long aluminum tube of radius
R. The time it takes the magnet to fall a
distance L depends on the tube radius as
a) 1/R
c) 1/R3
S
N
v
b) 1/R2
d) R
Hint: use conservation of energy!
Summary
• if current I is induced by the change in field B1, then the
direction of I is such that it creates a field B2 that
counteracts the change in B1.
• knowing the direction of I, it is easy to figure out the
sign of the emf ε.
Practice problems: Chapter 31, #26, 29, 44
Next lecture: read section 32.1
Physics 1E03 Lecture 26
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Physics 1E03 Lecture 26
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