What We’ve Observed• An increasing magnetic field
induces a negative emf• A decreasing magnetic field
induces a positive emf• A magnetic field that alternates
by increasing and decreasing causes current to move back and forth
Lenz’s Law• An emf (voltage) means there is
current flowing in the wire• How to determine direction of
current?• Heinrich Lenz: studied currents
moving in induced circuits• emf = - NA
Lenz’s LawHeinrich Lenz
Image obtained from: http://upload.wikimedia.org/wikipedia/commons/c/cc/Heinrich_Friedrich_Emil_Lenz.jpg
Lenz’s Law• A current induced by a changing B
field opposes the change in the B field• If B is increasing, current will
flow to try and decrease B field
B
⨡
B
⨡
Lenz’s Law• A current induced by a changing B
field opposes the change in the B field• If B is increasing, current will
flow to try and decrease B field
Binc.
⨡
Binduced
⨡
Binduced
⨡
I
⨡
×××
××× I
⨡
Binc.
⨡
Lenz’s Law• A current induced by a changing B
field opposes the change in the B field• If B is increasing, current will
flow to try and decrease B field
Binitial
⨡
Binduced
⨡
Binc.
⨡
Bnet
⨡
B still increases, but was opposed by B from induced current Negative feedback
Lenz’s Law• A current induced by a changing B
field opposes the change in the B field• If B is increasing, current will
flow to try and decrease B field• If B is decreasing, current will
flow to try and increase B field
B
⨡
B
⨡
Lenz’s Law• A current induced by a changing B
field opposes the change in the B field• If B is increasing, current will
flow to try and decrease B field• If B is decreasing, current will
flow to try and increase B field
Bdec.
⨡
Binduced
⨡
Binduced
⨡
I
⨡
I
⨡
Bdec.
⨡
Lenz’s Law• A current induced by a changing B
field opposes the change in the B field• If B is increasing, current will
flow to try and decrease B field• If B is decreasing, current will
flow to try and increase B field
Binitial
⨡
Binduced
⨡
Bdec.
⨡
Bnet
⨡
B still decreases, but was opposed by B from induced current Negative feedback
Lenz’s Law• A helpful analogy:• Inertia: mass resists
changes to its velocity• If velocity is = 0 m/s, wants
to remain at 0 m/s• If velocity is ≠ 0 m/s, wants
to keep moving with that velocity
B
⨡
B
⨡
Lenz’s Law• A helpful analogy:• Inertia: mass resists
changes to its velocity• If velocity is = 0 m/s, wants
to remain at 0 m/s• If velocity is ≠ 0 m/s, wants
to keep moving with that velocity
B
⨡
B
⨡
Lenz’s Law• A helpful analogy:• Inertia(?): charge resists
changes to its current• If velocity is = 0 m/s, wants
to remain at 0 m/s• If velocity is ≠ 0 m/s, wants
to keep moving with that velocity
B
⨡
B
⨡
Lenz’s Law• A helpful analogy:• Inertia(?): charge resists
changes to its current• If current is = 0 A, wants
to remain at 0 A• If velocity is ≠ 0 m/s, wants
to keep moving with that velocity
B
⨡
B
⨡
Lenz’s Law• A helpful analogy:• Inertia(?): charge resists
changes to its current• If current is = 0 A, wants
to remain at 0 A• If current is ≠ 0 A, wants
to keep flowing with that current
• Lenz’s Law describes how current in wires do this
B
⨡
B
⨡
Inductance• Suppose you have the following
circuit:• Inductor- resists changes in
current• If connected to source,
keeps current from flowing for a while• If disconnected from
source, keeps current flowing for a while
Inductance• Assume switch has just been
closed• Current flowing through
inductor was 0 A• Current now increasing
through inductor• Lenz’s Law: inductor opposes
change by inducing a current in opposite direction of increasing current• Acts like a temporary battery
Inductance• Assume switch has just been
closed• Current flowing through
inductor was 0 A• Current now increasing
through inductor• Lenz’s Law: inductor opposes
change by inducing a current in opposite direction of increasing current• Acts like a temporary battery
Inductance• After letting this run for a while,
inductor operates like a normal wire
Inductance• After letting this run for a while,
inductor operates like a normal wire• But what happens to a solenoid
with a current flowing through it?• Strong B field inside inductor
B
Inductance• Now suppose switch is opened B
Inductance• Now suppose switch is opened• Was current flowing through
inductor• Current now decreasing
through inductor• Lenz’s law: inductor opposes
change by inducing a current in same direction as decreasing current• Acts like a temporary battery
B
Inductance• Now suppose switch is opened• Was current flowing through
inductor• Current now decreasing
through inductor• Lenz’s law: inductor opposes
change by inducing a current in same direction as decreasing current• Acts like a temporary battery
B
Inductance• After letting this run for a while,
inductor operates like a normal wire
B
Inductance• After letting this run for a while,
inductor operates like a normal wire• Where did the current come
from?• Strong B field inside inductor
is no longer thereHmm…
Inductance• Inductors store energy in a B field• When current first flows into
inductor, some current gets stored in B field• When current is cut off, current
stored in B field released• Capacitors & Inductors• Capacitors store charge in E
field• Inductors store current in B
field
Inductance• Inductance:
L = Alternatively,V = L
• Units of inductance: Henry (H)
Inductance• Inductance:
L = Alternatively,V = L
• Units of inductance: Henry (H)
Image obtained from: http://en.wikipedia.org/wiki/Joseph_Henry#mediaviewer/File:Joseph_Henry_-_Brady-Handy.jpg
Joseph Henry
Inductance• Inductors in series:
Leqv = L1 + L2 + L3 + …• Inductors in parallel:
= + + + …
Image obtained from: http://en.wikipedia.org/wiki/Joseph_Henry#mediaviewer/File:Joseph_Henry_-_Brady-Handy.jpg
Joseph Henry
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