Faraday's Law & Induced EMF

Physics Lab 212

Faraday's Law & Induced EMF Software List Science Workshop

Equipment List

Science Workshop interface + voltage probes High inductance coil Stand and clamps Cardboard tube Meter stick or ruler Bar magnet Hookup wires with alligator clips Compass Tape Faraday's Law and Induced EMF

Summary of relevant concepts:

 A changing magnetic flux creates an induced electric field. These two quantities are related to each other by Faraday’s Law:   d  E ds   C dt  Note that the induced electric field exists even if there is no conductor present!

 If there is a conductor present, the induced electric field moves charges i.e. creates an induced current. We model this effect as an induced EMF given by: d EMF   dt  The DIRECTION of an induced current is such that it OPPOSES the change in flux that created it in the first place. Lab Activity: Faraday's Law & Induced EMF

Activity 1: Understanding Faraday's Law of Induction

The aim of this activity is to understand how a magnet moving near a coil of wire induces an emf.

 First, set up the experiment shown below. Examine which terminal of the induction coil is connected to the positive ("red") voltage probe and which one is connected to the negative (black) voltage probe.  Remember that you are going to induce an emf in the coil; examine the induction coil closely and note down how the coil is wound. Discuss and note down the relationship between the sign of the voltage measured by the voltage probes and the sense (clockwise or anti- clockwise) of the current when looking down at the coil from above.

Bar magnet

Induction coil Interface box

Analog channel A Cardboard tube  Start Science Workshop.  Click & drag the "analog plug" icon above to analog channel A and select the voltage probe measurement option when prompted.  Click & drag the "Graph" icon shown above to analog channel A.  Double click anywhere on the x-axis of the graph. When you do this, you will get a screen that allows you to set the parameters for the x-axis. Change the time settings to read "milliseconds" and set the maximum value to 3 seconds.  Double click anywhere on the y-axis of the graph. When you do this, you will get a screen that allows you to set the parameters for the y-axis. Set the maximum and minimum values of the voltage to +1 and -1 V, respectively.  Double click the "sampling options" icon.  The default rate at which the program measures data is 10 Hz. Change this to 1000 Hz.  Next, select "time" for "Stop condition;" this will open up a menu called "select stop condition;" enter "3" seconds. This means that data acquisition will stop after 3 seconds. Click OK.  Now, you are ready to take data!

Q1. Before you do the experiment, discuss amongst your group what you expect to observe as the magnet passes through the induction coil. Assume that the magnet is dropped with its N pole facing down. Sketch a qualitative expected plot of Voltage vs. Time below. Pay attention to whether voltages are positive or negative at some instant of time. Now, carry out the following experiment:  Use a compass to check which pole of your bar magnet is "North".  Position the cardboard tube so that the top is approximately 10 cm from the top of the induction coil. Hold the bar magnet with the N pole facing downwards, ready to be dropped through the tube.  Then, start recording data by clicking on the "REC" icon.  Drop the magnet and observe the graph of voltage versus time.

Q2. Sketch the graph below, with some indication of the values of the voltages observed. (Alternatively, you may print the graph and include it with your lab report.)

Q3. Use Faraday's Law to explain the shape of the graph. Remember the shape of the magnetic field lines of a bar magnet from your reading and lectures.

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______d Now, if we rewrite    in the following form,  dt  d and integrate both sides of the dt equation, we arrive at     dt , i.e. the flux is equal to the negative of the area under the voltage versus time graph. So, using Science Workshop analysis the previous graph to determine the incoming and outgoing flux.  In Science Workshop, click the previous graph to make it active.  Click the “Statistics” () icon to open the Statistics area on the right side of the graph. Click the “Autoscale” icon to rescale the graph to fit the data. In the Statistics area, click the “Statistics Menu” icon and select Integration from the menu.  In the Graph display, use the cursor to click-and-draw a rectangle around the first peak of the voltage plot. The area for the first peak will appear in the Statistics area.

Integration (first peak) = ______Vs

 In the Graph display, use the cursor to click-and-draw a rectangle around the second peak of the voltage plot. The area for the first peak will appear in the Statistics area.

Integration (second peak) = ______Vs

Q4. Is the incoming flux equal to the outgoing flux? Explain what you expect and compare it to the values calculated above.

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______Q5. Repeat the previous experiment with the magnet dropped from different heights: e.g. 2 cm, 5 cm, 15 cm, 25 cm and a few more positions for a total of seven or more different heights. Note down the values of any maximum or minimum voltages you observe in each case. Describe how the voltage versus time plots change when you change the initial height from which the magnets are dropped. Does the value of the incoming or outgoing flux change as the drop height is varied? Also, qualitatively explain your observations. Use sketches to illustrate the data.

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