EC-5c  Induction - Test Coil

OBJECTIVES:

1. To observe the emf induced in a small detecting coil by the varying magnetic field produced by the varying current in a separate large coil.
2. To follow how how this emf depends on the shape, and the frequency of the inducing current. The computer will produce a voltage varying with time in the form of a triangular waveform with amplitude V_max = 3 V and a frequency f = 10 Hz.

   Figure 5: The triangular waveform

   

INTRODUCTION:

1. The applied voltage varies linearly from V_min = - 3 V to V_max = 3 V in 50 ms. The slope of the voltage curve is therefore $\Delta$V/$\Delta$t = 120 V/s.
   The resistance of the large coil is R $\simeq$ 7$\Omega$ so current flowing in the large coil will vary linearly from I_min = - 3/7 = - 0.43 A to I_max = 3/7 = + 0.43 A in 50 ms, Correspondingly $\Delta$I/$\Delta$t = 17.2 A/s. The strength of the magnetic field produced by the large coil is proportional the the voltage applied on it, and therefore the rate of change $\Delta$B/$\Delta$t is proportional to the slope of the curve that shows the voltage versus time.

   YOU NEED TO KNOW: The emf induced in a coil is then $\cal {E}$ = - NA$\Delta$B/$\Delta$t where N is the number of turns in the small coil and A its cross-sectional area.

EQUIPMENT:

• PC and PASCO CI-750 interface.
• Power amplifier module.
• A stand holding a small detecting coil.
• Two large back-to-back coils with an ohmic resistance R = 7$\Omega$. The radius of the coil pair is r = 0.1 m. The output signal from the PASCO goes to the input of the Power Amp and then the output from the Power Amp goes to the large coil (using the RED and BLACK banana jacks).

PROCEDURE I: (10 min)

1. Click on the Launch EC-5c icon below (web version) to initiate PASCO software window. The monitor should now show a scope window and a window for the control of the signal generator. If necessary set the frequency to 10 Hz and the pull down menu to choose the triangular (or sawtooth) waveform. In the oscilloscope window set the trigger level to 1 V.
2. If necessary adjust the signal generator amplitude to 3 V.
3. Analog channels A and B are used to sense the voltage drop across the large coil (A) and the voltage induced in the small coil (B). Connect the banana jack wires RED to RED and BLACK to BLACK..
4. Turn on the signal generator by CLICKing on the ON button then initiate data acquisiton by CLICKing on the START icon. You should now see the voltage induced in the small coil together with the one applied to the large coil.
5. Adjust the size of the waves you see in the scope window using the size controls on the side of the scope window, then measure the height h₁ of the square wave using the cursor (5). Record this height.

   Figure 6: The layout with the Pasco CI and back-to-back coil assembly.

   

QUESTIONS

1. Explain why the induced voltage is a square wave.
2. Observe the direction of the winding in the large coil. What is the direction of the magnetic field during the rising part of the triangular wave? Explain your thoughts.
3. Observe the direction of the winding in the small coil. What is the direction of the induced emf during the rising part of the triangular wave? Explain your thoughts.

PROCEDURE II:

Move the small detecting coil 5 centimeters away from the large coil, measure the amplitude of the induced voltage. Repeat at distances of 10 and 20 centimeters. Make a simple graph using Microsoft Excel or any other suitable application.

QUESTION

How does the strength of the magnetic field depend on distance? $\sim$ 1/r ? $\sim$ 1/r²? $\sim$ 1/r³?

PROCEDURE III:

1.

Replace the detecting coil to its original position at the center of the large coil. Decrease the amplitude of the triangular wave to 2 V.

2.

Measure the height of the square wave and record this value.

QUESTIONS

Q1:

Did the slope of the triangular wave change? By how much?

Q2:

Is the change in amplitude of the square wave what you would expect? Why?

PROCEDURE IV:

1. Repeat procedure III with a frequency of 15 Hz.
2. Compare the result with those of procedure I and III

PROCEDURE V:

1.

Loosen slightly the clamp holding the small coil; rotate the coil 90^o so that it is in the horizontal plane. Observe the resulting induced voltage.

2.

Rotate the coil another 90^o so that it is in the vertical plane again. Observe the resulting induced voltage. Compare the result with procedure III.