Electromagnetic Induction Introduction We have seen that a separation of charge gives rise to something we have called an electric field. Further, we have seen that if we move those charges (separate or not), in the form of a steady current, we see something called a magnetic field that affects other moving charges. This already suggests a connection between electric and magnetic interactions. In the current lab, we will investigate another such connection discovered by the Englishman, Michael Faraday. He found (among a great many other things) that relative motion between a permanent magnet and a conductor resulted in a current in that conductor. Since currents are invariably due to electric fields, Faraday deduced that an electric field was induced in the conductor by the time varying magnetic field. Later, James Maxwell formulated this idea in terms of a changing magnetic flux. The result was Faraday’s Law of induction, given as: ∂Φ V = − m (1) ∂t where V is the induced voltage around a closed path and Φm is the magnetic flux passing through the area bounded by that closed path (refer to your physics text). The magnetic flux is defined as: Φ = ⋅ = Θ m B A BAcos (2) where B is the magnetic field strength, A is the area inside the path we talked about above, and Q is the angle between the field vector and the area vector (How can an area be a vector? Because physicists want it to be one – we define the magnitude of the area vector as …well, the area, and the direction as a perpendicular to the vector using the right hand rule – see your text, and we’ll talk about this in lab class). Equation 2 works for a uniform field (like inside a solenoid). In general, though, fields AREN’T uniform (like around a bar magnet or the Earth). In this case, you either need to learn calculus (so you can integrate), or just use an AVERAGE magnetic field in Equation 2 (that’s what we’ll do). Task 1) Plug the ends of a single wire into the ammeter. Move a permanent magnet toward and away from the loop. Vary the speed with which you move the magnet, and observe the effect on the current you measure. Wrap the wire into several loops and wave the magnet in and out of the center of the loops. Vary the speed with which you move the magnet. Reverse the magnet and shove the other end in and out. Comment on the difference. Compare the observations with a single loop to those concerning multiple loops. Comment on the dependence of the current you measure on the speed with which you move the magnet. Once you have a feel for things, estimate the voltage induced in the wire using the current you measure. Using this, estimate the total change in magnetic flux and with this result, estimate the strength of the field near the end of the permanent magnet. Task 2) Replace the loops of wire with a solenoid. Repeat the actions in Task 1). Compare this value of the magnet’s field strength to the previous one and discuss any differences. Comment on the differences and similarities between your observations in this section with those of the previous section. Task 3) Use nested solenoids to test Faraday’s law of induction. By running a current through one solenoid, you can generate a known magnetic field. By systematically varying that current, you can systematically vary the magnetic field and so the magnetic flux through the other solenoid. By measuring the current induced, you can infer the induced voltage. Repeat this, changing the rate at which the current is varied. Plot the induced voltage as a function of the rate of change of the magnetic flux through the second coil. Conclusion Report on the results of the lab, in which you address the questions raised above. Comment on the dependence between the induced voltage and the rate of change of magnetic flux revealed by your data (including the magnitude and sign of the slope). Describe a plan for implementing free market economies in the third world without displacing workers or interrupting the flow of goods and services. .