1. I2 is decreasing in magnitude I2 is constant
QUIZ lecture 17
Two current loops are perpendicular to the z axis and are centered on the this axis. Current I2 is counterclockwise. I1 is the induced current in the top loop. If I1 is counterclockwise, which statement is true? z I1 y x
I2 is decreasing in magnitude
I2 is constant
I2 is increasing in magnitude I2
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2. QUIZ lecture 16
Suppose a loop is placed in a uniform magnetic field and is spun around a vertical axis as shown. The loop makes one complete revolution every second.
The current induced in the loop
is zero
changes direction once per second
changes direction twice per second
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3. LECTURE 17
Motional EMF
Eddy Currents
Self Inductance

4. Example Problem: Solenoid within a Coil
120 turn coil of
radius 2.4 cm and
resistance 5.3 
solenoid with
radius 1.6 cm and n = 220 turns/cm
Initial current in the solenoid is 1.5 A.
Current is reduced to zero in 25 ms.
What is the current in the coil while the
current is being reduced?
What is the direction of the current in the coil?
Same direction as the current in the solenoid
Opposite the direction of the current in the solenoid
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5. Motional EMF
Motional EMF is any emf induced by the motion of a conductor in a magnetic field. v0
X X X X X X X X X B + - F
Fb = qv0B
Charge Separation
Current flows counterclockwise….
Resulting in a magnetic force F pointing to the left
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6. Calculation
A thin conducting rod is pulled with velocity v along conducting rails that are connected by a resistor, R. A uniform magnetic field B is directed into the page. Surface S is increasing therefore flux is increasing. What will be the magnitude & direction of the induced current?
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7. Energy Conservation
Rate of work by applied force:
The induced current gives rise to a net magnetic force F in the loop which opposes the motion:
External Agent must exert equal but opposite force FR to move the loop with velocity v; therefore, agent does work at rate P:
Energy is dissipated in circuit at rate P’:
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8. Question
Two identical conducting bars are moving through a vertical magnetic field (blue arrows). Bar 1 is moving vertically and Bar 2 is moving horizontally.
Which of the following statements is true?
A motional emf exists in the bar for case 1, but not for case 2.
A motional emf exists in the bar for case 2, but not for case 1.
A motional emf exists in the bar for both cases 1 and 2.
A motional emf does not exist in either bar v 1 2
Answer is B
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9. Eddy Currents
*Relative motion between a B field and a conductor induces a current in the conductor.
*The induced current give rises to a net magnetic force, FM, which opposes the motion.
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10. Eddy Currents
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11. Eddy Currents
During the last lecture we considered currents confined to a loop or a coil.
Electrical equipment contains other metal part which are often located in changing B fields. Currents in such parts are called Eddy currents
B field into the page v
Induced current anti-clockwise
Induced current clockwise
Flux increasing
Flux decreasing F
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
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12. Demonstration: Eddy Currents
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13. Reduce Eddy Currents Metal strips with insulating glue Cut slots into
DEMO: Lenz’s Law
Metal strips with insulating glue
Long tubes with bar magnets
Cut slots into
the metal.
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14. Quiz lecture 17
A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of the magnetic field, through the magnetic field, and then entirely out of the field on the right side? I . A B C t I v t
B is out of the page I t
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15. Inductors & Inductance
*An inductor can be used to produce a desired B field.
Symbol for inductor
*Inductance:
Units of L:
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16. Self Inductance
An induced emf, L, appears in any coil in which the current is changing.
X X
X X X a b
dI/dt
Self-Induction: Changing current through a loop induces an opposing voltage in that same loop.
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17. Self Inductance in a Coil
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18. Magnetic Energy in an Inductor
Upon closing switch, S, apply Kirchoff’s loop rule:
Multiply through by I:
power
delivered
by battery
power
delivered
to inductor
power
dissipated
by resistor
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19. Magnetic Energy in an Inductor
energy stored in
an inductor
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20. Magnetic Energy in a Solenoid
Both of
these are
general
results.
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21. Quiz lecture 17
The figure shows an emf L induced in a coil. Which of the following can describe the current through the coil: L
1. constant and rightward
2. constant and leftward
3. increasing and rightward
4. decreasing and rightward
5. increasing and leftward
6. decreasing and leftward
3 & 6
1 & 6
3 & 4
4 & 5
2 & 4
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