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Lecture 13.2 :!Inductors

Lecture Outline:!Induced Fields!

Inductors!LC Circuits!LR Circuits!

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April 9, 2015

Textbook Reading:!Ch. 33.6 - 33.10

Announcements

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•HW #10 due on Tuesday, April 14, at 9am.!

•Exam #3 next Thursday, April 16. Will cover Ch. 32 and Ch. 33. Bring your calculators and one sheet of notes.!

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Last Lecture...

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All induced currents are associated with a changing magnetic flux. Two ways flux can change:!1.Geometry: Loop can expand, contract, or rotate.!2.Magnetic field can change.

E =

����d�m

dt

���� =

������B · d

�A

dt+ �A · d

�B

dt

�����

Last Lecture...

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We know from Lenz’s law that a conducting loop in a changing magnetic field will develop an induced current to counteract the changing flux. There must be an E-field present to create this current in the loop.

In this changing magnetic field, the E-field is present whether or not the loop is there!

Clicker Question #1

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The induced emf around this loop is !

A. 200 V. B. 50 V. C. 2 V. D. 0.5 V. E. 0.02 V.

Clicker Question #1

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The induced emf around this loop is !

A. 200 V. B. 50 V. C. 2 V. D. 0.5 V. E. 0.02 V.

Clicker Question #1

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The induced emf around this loop is !

A. 200 V. B. 50 V. C. 2 V. D. 0.5 V. E. 0.02 V.

Is the induced current flowing clockwise or counterclockwise?

The Can Crusher Demo

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The Can Crusher Demo

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Equipment: • Electromagnetic Can Crusher • Stopwatch • Launch Support Rod • (2) Empty Soda Cans

ELECTROMAGNETIC CAN CRUSHER 5K20.65 Electricity and Magnetism Electromagnetic Induction Eddy Currents

Concept: This popular demonstration uses induction to crush a can with a loud pop. It can also be used as a can launcher as in the Jumping Ring demo. When the can is placed well within the coil that produces the B-field, the dominant component of that field is directed axially upward as shown above. The radially directed crushing force, F, is thus

F = IL ! B

where I is the induced current in the can with direction given by Lenz’s Law, L is the current segment length in the direction of the current, and B the coil’s magnetic field. When used in the launch mode, the can is repositioned upward to capture the fringing field and its radial component provides a vertical launching force (see 5K20.30 – Jumping Ring).

UCI PHYSICS AND ASTRONOMY Lecture Demonstration Program Updated 1/27/10

Procedure: Can Crusher: 1. Verify that the switch is toggled down before plugging in the power cord.

2. Drop a can fully into the tube-shaped holder. 3. Toggle the switch up to charge the crusher.

4. Using the stopwatch, charge the crusher for no more than 120 seconds.

5. Toggle the switch down to crush the can.

Can Launcher: 1. Place the launch support rod inside the tube-shaped holder and set the can on the support so that it sits

mostly outside the tube. 2. Repeat steps 3-5 above to launch the can.

Induced Fields

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We now understand that a changing magnetic field creates an electric field (even though no charge is present). We can rewrite Faraday’s law to allow calculation of the electric field.

Wclosed curve = q

��E · d�s

(Work done moving a charge around a closed-

loop in an electric field E)

Induced Fields

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We now understand that a changing magnetic field creates an electric field (even though no charge is present). We can rewrite Faraday’s law to allow calculation of the electric field.

Wclosed curve = q

��E · d�s

(Work done moving a charge around a closed-

loop in an electric field E)

E =Wclosed curve

q=

��E · d�s

Potential difference (EMF) crossed around that

closed-loop path.

Induced Fields

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We now understand that a changing magnetic field creates an electric field (even though no charge is present). We can rewrite Faraday’s law to allow calculation of the electric field.

Wclosed curve = q

��E · d�s

⇥�E · d�s = A

����dB

dt

����(for the case of an unchanging loop

perpendicular to B-field)

(Work done moving a charge around a closed-

loop in an electric field E)

E =Wclosed curve

q=

��E · d�s

Potential difference (EMF) crossed around that

closed-loop path.

Induced Fields

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Inside a solenoid, a changing magnetic field induced an electric field that circles around the magnetic field.

Induced Fields

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Inside a solenoid, a changing magnetic field induced an electric field that circles around the magnetic field.

Induced Fields

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Inside a solenoid, a changing magnetic field induced an electric field that circles around the magnetic field.

Induced Fields

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Maxwell knew of Faraday’s work, and based on symmetry he proposed that a changing electric field induces a magnetic field.

Induced Fields

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Maxwell (~1855) also predicted that electromagnetic waves with transverse E and B fields would travel at the speed of light.

vem wave =1

⇤�0µ0

⇥ 3.0� 108m/s

Induced Fields

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Maxwell (~1855) also predicted that electromagnetic waves with transverse E and B fields would travel at the speed of light.

vem wave =1

⇤�0µ0

⇥ 3.0� 108m/s

Inductors

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Inductors are devices in circuits that can be used to store energy in magnetic fields (similar to Capacitors storing energy in electric fields). They have interesting behavior when placed in circuits.

L � �m

I

1 henry = 1 H � 1 Wb/A = 1 Tm2/A

Inductance

Inductors

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What’s the inductance of an N turn solenoid?

Bsolenoid =µ0NI

l

Recall (from Ampere’s Law):

Inductors

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If (and only if) the current through an inductor is changing, a potential difference develops across the inductor.

Induced currentInduced field

Inductors

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If (and only if) the current through an inductor is changing, a potential difference develops across the inductor.

Induced currentInduced field

Inductors

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If (and only if) the current through an inductor is changing, a potential difference develops across the inductor.

�VL =

����d⇥m

dt

���� = L

����dI

dt

����We choose same sign convention as

in resistors...voltage decreases in direction of current flow.

Induced currentInduced field

Clicker Question #2

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Which current is changing more rapidly? !A. Current I1. B. Current I2. C. They are changing at the same rate. D. Not enough information to tell.

Clicker Question #2

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Which current is changing more rapidly? !A. Current I1. B. Current I2. C. They are changing at the same rate. D. Not enough information to tell.

Inductors

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Inductors

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How much energy is stored in the magnetic field of an inductor?

LC Circuits

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A circuit with an inductor and capacitor arranged in series is called a LC circuit. The current in this circuit will oscillate in time.

LC Circuits

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LR Circuits

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A circuit with an inductor and resistor arranged in series is called a LR circuit.

Reminders

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•HW #10 due on Tuesday.!•Exam #3 next Thursday.