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