Interlude: The Hardest Part of this Course

Faraday’s Law

We will do this twice, today and in about a month

(discovered Aug 29,1831)

Today’s Objectives

Introduce key concepts from electricity and magnetism through discovery activities, experiments, concept questions, discussion, and visualizations.

Later in the course, we will return to the same concepts.

Today we are just going to have some fun.

What we are trying to get a feel for:

You Tube Link: http://youtu.be/YywaJkGKOaY

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Concept Question: Loop in Uniform Field

While a rectangular wire loop is pulled upward though a uniform magnetic field B field penetrating its bottom half, as shown, there is

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1. a current in the loop.2. no current in the loop.3. I do not understand the concepts of current and

magnetic field.4. I understand the concepts of current and magnetic field

but am not sure of the answer.

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Demo: aluminum sleeve moving past fixed magnet, students do

this at their tables

Demo: we show the demo of magnet falling through plastic

tube and aluminum tube

Seeing the Unseen:

Faraday’s Law AppletApplet -- Faraday’s law applet (with a magnet and a coil):http://web.mit.edu/viz/EM/visualizations/faraday/faradaysLaw/faradayapp/faradayapp.htm

Play with the application until you are familiar with all the features. In the Actions Menu: try both Manual and Generator Mode. You can use the buttons at the bottom to start, pause and reset the simulation. You can move the magnet and the ring back and forth using the mouse. Let each person in the group have a turn.

Seeing the Unseen: First Concept Flow

Group Discussion Question

What are some examples of flow of “something” through an area?

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Examples of FlowElectric Current: Flow Of Charge

Electric Current I: Charge ΔQ flowing across area A in time Δt

I

ΔQ

Δt

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Current and Magnetic Field

Current produces a magnetic field as shown in figure

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Magnetic Field of Bar Magnet

(1) A magnet has two poles, North (N) and South (S)(2) Magnetic field lines leave from N, end at S

Seeing the Unseen:

Magnetic Field

Run the Applet on generator mode and stop the magnet when it is near the ring

Scroll down on the panel on the right and click on Magnetic Field: Iron Filings

Seeing the Magnetic Field: Iron Filings

The iron filings represent the magnetic field present at the instant you stopped the magnet . The direction of the magnetic field is along the direction of the iron filings. Does the magnetic field intercept the area of the circular wire?

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Magnetic Flux Thru Wire Loop

BB A

Flux is the Generalization of Flow

Product of magnetic field and area

Discussion Question: Magnetic Flux in Ring

The first graph on the right in the Applet shows a plots of the external magnetic flux and total magnetic flux in the ring versus time. Briefly describe where the “external flux” (red plot) is coming from: that is, what kind of flux is this, what creates it, over what area is the flux being measured.

More Discussion Questions About Magnetic Flux

1. Describe different ways that you can change the external flux

2. Explain how the total magnetic flux (blue plot)

is related to the external magnetic flux (red plot).

Current in Ring

The second graph on the right in the Applet shows a plot of the current in the ring versus time.

Proposing a Hypothesis

Propose a qualitative relationship between magnetic flux (seen in top graph) and current that flows in the ring (seen in bottom graph).

Testing Hypotheses

Groups utilizing the application came up with the following hypotheses.

1.Group A conjectured that the current through the ring is proportional to the total magnetic flux.

1.Group B proposed that the current through the ring is proportional to the change in the total magnetic flux.

Use the application to test these two hypotheses. Design and run a virtual experiment that could rule out any of the hypotheses. Which did you rule out and why?

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Faraday’s Law of Induction

I :

dB

dt

d(BA)

dt

dB

dtA

Changing magnetic flux induces a current

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Electromotive Force

Electromotive force looks like a voltage difference. It’s a “driving force” for induced current

IR

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Faraday’s Law of Induction

:

dB

dt

d(BA)

dt

dB

dtA

Changing magnetic flux is proportional to electromotive force

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Demo: Electromagnetic Induction

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Demo: Electromagnetic Induction

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Demonstration: Induction

At this point, students again move the coil of wire in their

experiment just to observe the current

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Concept Question: Loop in Uniform Field

While a rectangular wire loop is pulled upward though a uniform magnetic field B field penetrating its bottom half, as shown, there is

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1. a current in the loop.2. no current in the loop.3. I do not understand the concepts of current and

magnetic field.4. I understand the concepts of current and magnetic field

but am not sure of the answer.

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Concept Question Answer: Loop in Uniform Field

Answer: 1. The motion changes the magnetic flux through the loop. The magnetic flux is decreasing in time as more of the loop enters a region of zero magnetic field. According to Faraday’s Law there is an induced current through the loop.

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Concept Question: Loop in Uniform Field

While a rectangular wire loop is pulled sideways though a uniform magnetic field B field penetrating its bottom half, as shown, there is

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1. a current in the loop.2. no current in the loop.3. I do not understand the concepts of current and

magnetic field.4. I understand the concepts of current and magnetic field

but am not sure of the answer.

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Concept Question Answer: Loop in Uniform Field

Answer: 2. The motion does not change the magnetic flux through the loop. The magnetic flux is constant in time. According to Faraday’s Law there is no induced current through the loop.

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Concept Test: Induced CurrentWe define positive current clockwise as viewed from the top. As the coil moves from well below the magnet to well above that magnet, the induced current through the coil will look like:

(1) (2)

(3) (4) (5) I don’t know

Try to answer this question using your experimental set-up

Concept Question: Induced Current Answer

Solution (3).

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Lenz’s LawDirection of Induced Current

Discussion Question: Induced Current

Run the Applet and observe the relation between the sign of current and the slope of the plot of magnetic flux. What do you observe?

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Minus Sign? Lenz’s Law

Induced EMF is in direction that opposes the change in flux that caused it

dB

dt

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Conclusion: Faraday’s Law of Induction

dB

dt

Changing magnetic flux generates electromotive force that opposes that

change in flux

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Jumping Ring

An aluminum ring jumps into the air when the solenoid beneath it is energized

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What is Going On?

This is a dramatic example of Lenz’s Law: When the magnetic field created when the solenoid is energized tries to permeate the

conducting aluminum ring, currents are induced in the ring to try to keep this from happening!