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Motional EMF
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A I, B ii, Ciii.

1. Clockwise
2. zero

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What is the direction of the magnetic field
produced by this current loop inside the
loop?A upwardB downward
I is CW from above
B
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Note the splay in the field lines!
Viewed from above, current in the loop A will
flow clockwise B will flow counterclockwise C
will not flow at all
A
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Consider vxB. Since the field lines splay, vxB
is CW from above. The current in the loop
causes a downward B field inside the loop. The
flux of this induced B field Opposes the flux
change that would otherwise occur. Lenzs
Law Induced current is CW, seen from above, by
RHR.
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Viewed from above, current in the loop A will
flow clockwise B will flow counterclockwise C
will not flow at all
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The flux through the loop is downward and
decreasing. To oppose this change, we need the
current in the loop to flow CLOCKWISE, seen from
above. (Again, if the loop is moving, you can
use vxB to find the direction of the force. But
you have to remember that the field lines are
getting farther apart farther from the magnet.)
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We saw that, when we move the loop down, a CW
current flows, owing to the B field acting on the
(downward moving) charges. If, instead, we move
the magnet UP, keeping the loop still,
current A will flow clockwise (viewed from
above) B will flow counterclockwise C will not
flow all, since B fields dont act on stationary
charges.
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While its true that B fields dont act on
stationary charges, it really shouldnt matter
which object is moved! Lets do the experiment!
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Changing magnetic fields DO result in the motion
of stationary charges. Thus, changing magnetic
fields must induce electric fields. (It is
perhaps better to say that changing magnetic
fields are coupled to electric fields.)
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The four cases
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What can we say about the induced E field?
Like with Amperes law, we can only find E from
this easily when there is A LOT of symmetry. E
must (by symmetry) be the same everywhere, or
zero, in our loop. (In cases without symmetry,
there is still an E field we just dont have the
math tools to find it.)
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• Examples where we can easily find E from a
  changing magnetic field.
• Circular loop, N pole of magnet, with change of
  flux specified.
• A very long (infinite) solenoid, with ramping
  current (and B field)

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A loop of copper wire is shown. Moving the magnet
up A causes increasing upward B flux B
causes decreasing upward B flux C causes
decreasing downward B flux D causes increasing
downward B flux E has no effect on the flux
through the loop
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A loop of copper wire is shown. Moving the magnet
up -causes increasing upward B flux. In what
direction should the B field caused by the
induced current be? A up B down
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A loop of copper wire is shown. Moving the magnet
up -causes increasing upward B flux. The loop
current should oppose the flux change. So the
field from the loop current should be DOWN. What
direction does the current flow, viewed from
above? A CW B CCW
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A loop of copper wire is shown. Moving the magnet
up -causes increasing upward B flux. The loop
current should oppose the flux change. So the
field from the loop current should be DOWN. The
induced current must flow CW, seen from above, by
the RHR.
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What is the direction of the induced current in
the ring, as seen from above? A CW B CCW C
There is no induced current
A
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Considering the magnetic field of the solenoid as
a magnet The top of the solenoid is a A N B
S pole
A
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Considering the magnetic field of the loop as a
little magnet the North pole of the loop is A
up B down
B
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The magnetic force between the solenoid and the
coil should be A attractive B repulsive C
zero
B
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Generators
At this instant, current through the light bulb
will flow A left to right in side view B
right to left in side view C not at all
A
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Generators
At this instant, current through the light bulb
will flow A top to bottom in side view B
bottom to top in side view C not at all
C
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Lets do the math for a rotating loop in a
uniform B field.
B
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More about motional EMF
A square loop is pulled through a constant B
field. What is the magnitude of the motional
emf? A 0 B vBL C 2vBL D vBL2
A
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More about motional EMF
Although there is magnetic flux through the loop,
the amount is NOT changing with time. So emf
0.
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Here, the left side is not moving, so there is no
magnetic force on the initially stationary
charges on that side. There is magnetic force on
the charges on the right side, pushing positive
charges up. Each charge acquires an energy
qvBL force x distance. That energy is then
lost as the charge slides downhill, through the
lightbulb, heating it. Where does the energy
come from that lights the bulb? It cannot come
from the B-field, as that is unchanging while the
bar is sliding. Answer you must use force to
pull the right side at constant v. How much
force?
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More on Solenoids
Long solenoids have spatially uniform B inside
(from Amperes law) If the current is increased
linearly with time, the B field will increase
linearly with time. In this case, the field is
out of the page (top view) and increasing with
time. If this is done, what will be the direction
of the induced E field at point b, distance r
from the axis? On the top view A up B down
C left D right E out of the page
B
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More on Solenoids
Consider a loop at a radius r. The flux is upward
and increasing, so the induced EMF must be such
as to cause a downward B field if a loop of wire
were there. So the EMF must be CW (from above)
and E must point downward (top view.) Lets do
the math.
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More on Solenoids
What is the induced E field at point a, on the
solenoid axis? A 0 B not zero
A
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More on Solenoids
What is the induced E field at point c, outside
the solenoid, where B is essentially zero? A
0 B not zero, upward (top view) C not zero,
downward (top view) D not zero, leftward(top
view)
.c
B
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Now consider 4 loops, all with the same area. The
B field is increasing with time. What is true? A
loops a,b,c have the same ?, but d has less. B
loops a and c have ? 0, but b and d have same
nonzero ?. C loop a has ? 0, but b,c,d have
the same, nonzero ?. D loop c has ? 0, loop a
has a little, b has more, and d the most. E loop
c has ? 0, but loops a,b,d all have the same
nonzero ?.
E
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Mutual Inductance Inductors
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Electric Toothbrush - Recharges via mutual
induction
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Resistor opposes motion (current), like
friction Inductor opposes change in motion,
like inertia
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Do not confuse cause and effect. The voltage
drop from a to b (in part c) is an effect of the
increasing current. Something has to overcome
(meaning provide) this voltage drop if the
current is to increase. Think of the back EMF
this way if you replace the inductor with a
battery, the battery (by itself) would drive
current that would oppose the change.
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Immediately after closing the switch, where is
the potential higher?A AB BC Potential
at A B is the same
A
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A very long time after closing the switch, where
is the potential higher?A AB BC
Potential at A B is the same
C
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After the switch has been closed a long time and
a steady state reached, the switch is opened.
Where is the potential higher?A AB BC
Potential at A B is the same
B
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Archuleta C Herrera Es Martinez Middleton Sinyenko
Warren Wildau
Wed Dec 1, 2010 Which curve shows the current
after switch s1 is closed? B
Lets calculate
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Which curve shows the voltage drop across the
inductor after S1 is closed? C
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Which curve shows the voltage drop across the
resistor after S1 is closed? B
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After reaching a steady current, S1 is opened and
S2 is closed, simultaneously. What curve shows
the voltage drop (from a to b) across the
resistor vs time? C
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After reaching a steady current, S1 is opened and
S2 is closed, simultaneously. What curve shows
the voltage drop (from b to c) across the
inductor vs time? D
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A little while (tL/2R) after the switch is
closed, what is the voltage around the circuit? C
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What is the voltage around the circuit a long
time after the switch is closed? B
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Switch s1 is closed. Just after, what is the
current through the resistor? A A 0 B
E/R C E/(RL) D E/(RC)
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Just after closing switch S1, what is the voltage
drop across the inductor? B A 0 B E C
E/2 D E/L
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A long time after closing switch S1, what is the
charge on the capacitor? B A 0 B CE C
E/C DE/(RC)
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Amperes law
This completes Maxwells Equations
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LC Oscillations
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A B - C 0
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A electric B magnetic
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A B - C 0
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Inductor exerts electric force on the charges
(induced EMF is an electric field.)
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Immediately after closing switch, what is current
through inductor? A 0 B 1/2 ampere C 1
ampere D 2 amperes
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Immediately after closing switch, what is voltage
across capacitor? A 0 V B 20 V C 40 V D
160 V
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No current through inductor, no voltage across
capacitor!
Immediately after closing switch, what is current
through battery? A 0 B 1/2 ampere C 1
ampere D 2 amperes
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No current through inductor, no voltage across
capacitor!
Immediately after closing switch, what is di/dt
for the inductor? (Be careful!) A 0 B 20
kA/s C 40 kA/s D 0.5 kA/s
What would be the answer if there were no cap in
parallel? C
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A long time after closing the switch, what is the
current through the capacitor? A 0 B 1/2
ampere C 1 ampere D 2 amperes
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A long time after closing the switch, what is the
current through the inductor? A 0 B 1/2
ampere C 1 ampere D 2 amperes
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Critical damping gives the fastest return to
equilibrium
Also applies to car shocks springs!