1 Physics 241 Lab – Matt Leone Week 10: The Leopard and the Muskrat! [email protected] (email preferred), PAS 376, o. 520-621-6819 Office Hours: M & W 11:00-11:50, or by appointment. Consultation Room (PAS 372): F 12:00-12:50 http://bohr.physics.arizona.edu/~leone/phy241/phys241lab.html General Comments: • Today we will study how a changing magnetic field creates a changing electric field, and how that changing electric field will make the charges in a conductor move. I.e. current is caused by an oscillating magnetic field. Lab 10 – Theory. Magnetic field from current: When the current in a circuit is changing, the magnetic field created by the current is also changing. You have already learned to use Ampere’s Law to find the magnetic field inside a current carrying loop (chapter 30): • Ampere’s Law for a current loop: ! Binside=µoICcircumference, so that for a solenoid made of N loops, • Ampere’s Law for a solenoid: ! Binside=NµoICcircumference So if you know what the current is doing, the number of windings of a solenoid, and the radius of the solenoid, then you can tell the magnetic field inside the solenoid. Also, use the right-handed screw rule to find the direction of the magnetic field produced. Let me show you (DEMO). Summary: A solenoid with a constant current produces a strong magnetic field inside its coils. If the current is oscillating back and forth, so is the magnetic field within. Voltage from changing magnetic field: If a magnetic field is changing through the area of a circuit, then Faraday’s law says that this changing magnetic flux will induce a negative voltage in the circuit: • Faraday’s law: ! Vinduced= "d#Bdt, where the magnetic flux is simply • Magnetic flux: ! "B=r A area•r B . Since the area of a fixed circuit is constant, this means that • Faraday’s law for fixed area: ! Vinduced= "AdBdt. The negative sign is supposed to tell you something about the direction. I prefer to use Lenz’s Law to figure out the direction, which I will discuss after a moment. In a conductor, this induced voltage causes current to flow. Summary: A changing magnetic field produces a voltage (induced EMF) in a circuit, which in turn causes a current to flow.2 Putting concepts together: 1 + 1 = 2. If you take a solenoid and drive it with an alternating current, it will produce an alternating magnetic field inside its coils. If you then take another solenoid that is unpowered and place it nearby so that the changing magnetic field of the first solenoid is inside the coils of the second solenoid, then a voltage will be induced in the second solenoid despite the fact that they in no way touch each other. This is the process of mutual inductance. The definition of the mutual-inductance, M (the muskrat), is: ! M1 to 2=Vinducedin circuit 2"dIcircuit 1dt. Basically, if the Muskrat sees the Iguana moving under the Vulture, and it too pounces. Similarly, you usually use the rearranged equation to find the induced voltage in the other circuit ! Vinducedin circuit 2= "dIcircuit 1dtM1 to 2. Lets look at an example (DEMO). 1 + 0 = 1. This gets tricky. If you take a single solenoid and apply an alternating voltage, then it with have an alternating current. The alternating current of this single solenoid will produce an alternating magnetic field inside its own coils. Now, there is a changing magnetic field inside the coils of this single solenoid. The changing magnetic field induces a voltage in this single solenoid that opposes the applied voltage. Therefore, the alternating voltage applied to this solenoid through a chain of concepts causes an opposite voltage inside the solenoid that decreases the total current. This very weird process is called self-inductance. The definition of the self-inductance, L (the leopard), is similar to the resistance: ! Lcircuit 1=Vinduced incircuit 1"dIcircuit 1dt. Basically, if the Leopard sees the Iguana moving under the Vulture, it pounces. Of course you usually use the equation rearranged to find the induced voltage that opposes the driving voltage. ! Vinduced incircuit 1= "dIcircuit 1dtLcircuit 1. Lets look at an example (DEMO).3 Lenz’s Law and the right-handed screw rule: Now lets do some “simple” examples of a changing magnetic field inducing a current. Be sure to take good notes/solutions on these pictures below. (FOR A GRADE) Example A: Example B: Example C: Example D:4 Lab 10 – Procedure – write on this sheet and turn it in with your write-up. 1. Here you will examine the magnetic field produced by a solenoid. Note that a solenoid produces a magnetic field very similar to a bar magnet of the same shape. a. First check that your compass has not been flipped. The green arrow should point to the Earth’s south magnetic pole, which is located to the geographic north! Is it correct? If not, get my attention. YOUR ANSWER: b. Next check your bar magnet with your compass to see that it is labeled correctly. Remember that the green arrow points to the south magnetic pole. Is it labeled correctly? If not, get me and I will show you how to remagnetize it by placing it in the magnetic field of the solenoid and tapping it. YOUR ANSWER: c. Examine the direction of the windings of your solenoid. You can tell which way the current circulates by how the wire enters the solenoid. Apply constant current using the constant voltage supply (a few volts should be good) to your solenoid. Use the right-handed screw rule to predict the positive direction (north pole) of the magnetic field produced. YOUR PREDICTION: d. Test your initial determination of the field direction by measuring the magnetic field produced using your compass. Were you correct? If you are confused, get me. YOUR ANSWER: e. Draw a diagram below to explain what you have found. Include in your picture, the direction of the windings, the direction of the current, and some magnetic field lines. Be sure to draw the windings in a 3-dimensional way so I can grade your answer. YOUR DIAGRAM:5 2. Here you will test how a changing magnetic field induces a voltage in an upowered solenoid. WRITE ANSWERS WHEN INSTRUCTED (FOR A GRADE) a. Hook up your solenoid to the o-scope so you can measure the electric potential difference between both ends. b. Use a compass to double check the accuracy of the labeled north pole of your bar magnet.
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