Interactive Lecture Demonstration 9 – Faraday's Law

 

 

 

In this demonstration, a solenoid will be connected to an alternating current source. A smaller coil (called the "pickup coil") will be put in the middle of the solenoid. An oscilloscope will be connected to the pickup coil. According to Faraday's Law, the changing flux through the pickup coil of the magnetic field made by the solenoid will cause an induced emf in the pickup coil. We will use Faraday's Law to predict the magnitude of the induced emf, then measure the induced emf with the oscilloscope and compare with our prediction. The diagram below shows the setup.

 

 

 

 

 

 

 

 

 

 

 

 

  1. Every centimeter along the solenoid's axis has about 300 turns of wire. Suppose that we first connect the solenoid to a battery. If the battery supplies a current of 50 mA, calculate the strength of the magnetic field inside the solenoid (you'll need a formula from the textbook).

 

 

 

 

 

 

 

 

  1. The pickup coil has a diameter of about 2 cm and has about 400 total turns of wire. Calculate the magnetic flux passing through the pickup coil for the situation described in #1.

 

 

 

 

 

 

 

  1. What would be the magnitude of the induced emf in the pickup coil in the situation described in #1 ?

 

 

 

 

 

  1. We hope that your answer to #3 was "zero." According to Faraday's Law, the magnitude of the induced emf in the pickup coil is equal to the rate of change of the magnetic flux through the pickup coil. A battery provides a constant, direct (i.e. always in the same direction) current to the solenoid. If the current in the solenoid is constant, the magnetic field inside the solenoid is constant, and thus the magnetic flux through the pickup coil is constant. The rate of change of the flux is zero.

 

Now the solenoid will be connected to a source of alternating (changing direction) current. The source will make a "sawtooth" current. A graph of the current as a function of time is shown below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Use Faraday's Law, the formula for magnetic flux you derived in #2, and the formula for the solenoid's magnetic field you found in #1 to find a formula that gives the induced emf in the pickup coil in terms of the rate of change of the current in the solenoid.

 

 

 

 

 

 

 

 

 

 

 

 

  1. The alternating current source will make a current with a frequency of 20 Hz (this means that the current goes through a complete back-and-forth cycle 20 times per second). The maximum value of the current in either direction will be about 70 mA. Use this information and the graph above to calculate the rate of change of the current when the current is increasing (the rate of change during a decreasing part of the cycle will be equal but opposite).

 

 

 

 

 

 

 

 

 

 

 

 

  1. Finally, use your result from #6 and your formula from #5 to predict what the induced emf in the pickup coil should be, when the current in the solenoid is increasing.

 

 

 

 

 

 

 

 

 

 

 

 

  1. Predict what a graph of the induced emf vs. time should look like (what happens to the induced emf when the current through the solenoid is decreasing ?). Sketch your graph on the axes directly below the current vs. time graph for the solenoid. Put labels, numbers and units on both axes. Your time axis should use the same scale as the current vs. time graph.

 

  1. Now we will do the experiment to test our predictions. The oscilloscope will plot a graph of the induced emf vs. time. How does it compare with your predicted graph ? Note both the shape of the graph and the scales on the vertical and horizontal axes.