## Friday, July 1, 2011

### Introducing Basic Physics (Electromagnetic Induction) Pt. 23

We now move to investigating basic electro-magnetic induction. The discovery of the basis for it, by Michael Faraday, made sense after the earlier (1820) discovery of Oersted's (See Fig. 1) showing that magnetic fields can be produced from electric currents. As shown in this simple sketch, a confirmation can easily be done using a simple circuit setup, with wire piercing a piece of flat cardboard, on which is overlaid white paper to permit magnetic lines of force to be plotted. The easiest way to do this is by simply moving a sensitive magnetic compass around the wire and noting the directions of the needle.

The inverse effect, magnetism from electricity, was discovered by Faraday 11 years later in 1831. His finding was that the relative motion between a conductor and a magnetic field generated a small electric current detected in a sensitive meter (e.e. galvanometer). He found in his simple experiments that it made no diference whether a magnet was moved relative to a coil, or a coil moved relative to a magnetic. In either case electric current was produced. Today, the principle forms the basis of large power generators which use motion of large devices in powerful magnetic fields to form the basis of a dynamo and produce electricity.

In the experimental set-up we used at Harrison College, the following apparatus was used:

- U-shaped iron core (to be magnetized)

- Gilley coil -apparatus

- rheostat

- switch

- connecting wire

- d.c. emf source

- strong Alnico bar magnet (e.g. 10 gauss or more)

The circuit diagram for the experiment is shown in Fig. 3 with the apparatus indicated. What we have basically is a potential divider circuit to determine the direction of the galvanometer deflection for a known current direction.

Procedure:

1- Connect one Gilley coil in series with a key (k), rheostat and d.c. source in such a way that the current direction (+ to -) in the coil is clockwise as viewed from the side opposite the binding posts. Check the polarity of the electro-magnetic with the magnetic compass. (Does it conform to the right hand rule? I.e. when you extend your forefinger, thumb and second finger in mutually perpendicular directions to each other then your forefinger follows the magnetic field direction, your thuMb, the motion, and seCond finger the current)

2- Connect the other Gilley coil to the galvanometer terminals through the resistance decade box so the sensitivity of the meter can be varied.

3- Set the two coils back to back, and set the rheostat for minimum effect using the sliding wire on the divider. (The decade box is set to maximum). Close the switch at the key k and note the galvanometer deflection. Decrease the decade box setting as needed to get a good (e.g. half -scale) galvanometer deflection each time the key is open or closed.

4- Observe to see whether the induced current in the secondary coil is the same or in an opposite direction to that of the primary coil (connected to the d.c. source). Explain in terms of Lenz's law:

Lenz's law (a different form of the conservation of energy):

Any electromagnetically induced current will always be in a direction such that the magnetic field set up by the induced currents will oppose the motion that produced them.

Note the galvanometer reading as the switch is closed and then when opened. Explain both then repeat with the coils separated by about 1 inch (2.5 cm).

5- Set the coils up again as in (1) and close the switch. When the galvanometer needle comes rest move the slider quickly to maximum resistance (~ 100 ohms). Explain what happens. Now move the slider back to minimum resistance and note the result.

6- Now insert the soft iron core through both coils and close the switch again, noting the deflection. Explain.

7- Pull the coils 2 in. apart but with the iron core still inside. Close the swtich and note the deflection. Does the distance between the coils (when core is present) significantly affect the readings. Explain. Check the polarity of the secondary coil with the small compasss during the buildup of induced emf. Does it follow Lenz's law.

Quantitative aspects:

The magnitude of the emf is directly proportional to the time rate of change of magnetic flux. If the flux is constant, NO emf will be produced. The magnitude of the induced emf is given by:

E = {Nφ/ t} x (10^-8)

where:

E = avg. value of induced emf magnitude
N = no. of turns in the coil of wire.

φ = change of magnetic flux (in maxwells)

t = time for the change in flux to take place.

Example problem:

A conducting loop of 50 turns is used in an induced emf experiment. It is moved through a field of 60,000 mx in a time of one thousandth of a second. What is the average emf induced?

Solution:

φ = 60,000 mx

t = 0.001 s

N = 50

then:

E = Nφ/ t x (10^-8)

= [(50) (60,000)]/ 0.001 s x (10^-8) = 30 V

Other Problems:

1)a)A bar magnet is inserted into a coil of wire (see Fig. 4) and a galvanometer needle deflects showing an electric current was produced in the wire. The current is electrical energy. What os the source of this energy?

b) A bar magnet which has a field of 1,000 mx is used for the above exp. If it is inserted into a coil of 30 turns in a hundredth of a second, what is the emf produced? Would it be detectable on a galvanometer that reads from - 5 to 5 milli-amps? Explain.

c) Using the sketch from the diagram, indicate where magnetic N and S poles would appear in the coil.. Explain the reason for this.

2) Explain, on the basis of the experimental results, how it is that an electric generator may be rotated easily on an open circuit but becomes extremely hard to turn when it is connected to a load.

3) An alternative way to assess the magnitude of induced emf is by way of the formal equation: E = B Lv, where B is the magnetic flux density, L is the length of the displaced object and v the relative motion (velocity of moving agent).

Use the above to estimate the induced emf created when a copper bar 30 cm in length is initially perpendicular to a field B of flux density 0.8 weber/m^2 and moves at right angles to the field at a speed of 50 cm/sec.

4) A copper disc of 10 cm radius is allowed to rotate at 20 rotations per second about its axis and with its plane perpendicular to a uniform B-field of flux density 0.6 weber/m^2. Find the potential difference between the disc's circumference and its center. (Hint: The magnetic flux threading a uniform disc is φ = BA where A is the area of the disc.)