Introduction: Recall what the Biot-Savart Law and, more generally, Ampere s Law say: Electric Currents Create Magnetic Fields

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1 Electromagnetic Induction I really don t like the order in which your author presents the material in this chapter, so I m going put in a slightly different order. Introduction: Recall what the Biot-Savart Law and, more generally, Ampere s Law say: Electric Currents Create Magnetic Fields Also, remember this was discovered accidentally by Oersted in For some years after, people wondered about the inverse of this process: Can Magnetic Fields Create Currents? If the magnet and the coil just sit there, then there is no current. In 1831, Michael Faraday (English) and Joseph Henry (American) made another accidental discovery. Turning the current on and off in one coil induces a current in the other. PhET EM PhET coil PhET trans How are the two coils connected? By a Magnetic Field.

2 Faraday s Experiments Faraday went on to thoroughly study this to find what aspect of the magnetic field can induce a current in a loop. Experiment: Observations: 1.) Magnet and coil motionless: No Current Mag & coil 2.) Magnet moving toward the coil: Current in one direction Magnet moving away from the coil: Current in the opposite direction Reversing the polarity of the magnet reverses the direction of the current. 3.) Coil moving toward the magnet: Coil moving away from the magnet: Current in one direction Current in the opposite direction This case is not surprising. Here, we have charges moving in a magnetic field, so they will feel a force. This is called Motional EMF. However observation #2 above can t be explained as motional EMF. 4.) Two coils with one switched on and off Brief Current PhET trans

3 Faraday s Law Faraday realized that all of these experiments have one feature in common: There is an induced current in the light bulb coil when the magnetic field through the coil is changing. Faraday was also able to deduce a quantitative description of this: Faraday s Law: Conducting Loop with resistance R The Induced EMF* in the Loop is: The Induced EMF then causes an Induced Current: *The absolute value sign is there because Faraday s Law in this form doesn t tell us anything about the direction of the induced EMF or current; for that we ll need Lenz s Law (coming soon).

4 What About Magnetic Flux? Back in chapter 27, we used the flux of the electric field in our work with Gauss Law. Everything that we learned about the electric flux there also applies to the magnetic flux here. All we have to do is: Then all of the equations and the ways we calculated the flux of the electric field in chapter 27 will work for flux of the magnetic field as well. The following two slides are the exact same slides that we used in chapter 27 but changed to the magnetic flux using the above replacements:

5 Flux of the Magnetic Field Flux is a measure of how much a magnetic field passes through a 2D surface. Flux depends on the size and direction of the field and the size, shape, and orientation of the surface. Your author starts with flux for special cases and builds to a general definition; read his account, we ll do the opposite: Flux for the General Case (any field, any surface) Magnetic Flux: 2D surface (New, different for magnetic!) Element of area Note: this is called a surface integral

6 Special Cases of Flux (we ll use these a lot) Uniform Magnetic Field & Planar Surface: Uniform Magnetic Field & Planar Surface perpendicular to the field: For either of these cases, the relation to remember is:

7 PhET Computer Lab: Faraday s Law Using the group s computer, one of you log onto masteringphysics and begin the exercise: PhET Faraday s Law. Use the computer to complete the exercise, but record your answers on the sheet to hand in that s what will be graded. When you re done with the exercise, make sure your Group s name and all of your names are on it, and turn it in. Feel free to play with the simulation if you have time. Or, play with some of demos set up on the table. Anytime you want play with the PhET simulations, just go to:

8 The induced EMF: Back to Faraday s Law* And the magnetic flux is: Where S is the surface of the conducting loop. The induced EMF is given by the rate Faraday s Law says: at which the magnetic flux is changing. What can produce a changing flux? Any of these can occur simultaneously we ll see problems like that! *By the way: Faraday s Law is our 4 th Maxwell Equation, but we ll want to write it in a different form on Monday.

9 Whiteboard Problem: 30-1 A 1000-turn coil of wire has a diameter of 1.0 cm and is in a uniform magnetic field that increases from 0.1 T to 0.3 T in 10 ms. The axis of the coil is parallel to the field. What is the EMF in the coil? (LC) Your sketch should look like this: N = 1000 turns (i.e. loops)

10 Whiteboard Problem: 30-2 The loop in the figure is being pushed into the 0.2 T magnetic field at 50 m/s. The resistance of the loop is 0.1 Ohms. What are the magnitude and direction of the current in the loop? (LC, magnitude) How can you figure out which way the induced current goes, clockwise or counterclockwise?

11 Faraday s Law: Lenz s Law Conducting Loop with resistance R Lenz s Law can be used to find the direction of the induced current: This is a very odd physical law no equations, just words. The most important step in applying Lenz s Law is to ask: What is the Flux doing, increasing or decreasing? Let s go back to Problem WB30-2 and figure out which way the induced current goes.

12 Whiteboard Problem 30-3 The figures below show a 10 cm diameter loop in a magnetic field. The loop s resistance is 0.20 Ohms. What are the magnitude and direction (LC: CW or CCW) of the induced current in the loop? (LC: CW or CCW) (LC: CW or CCW) (LC: CW or CCW)

13 Whiteboard Problem 30-4 A 100 turn coil with a diameter of 2.0 cm and resistance 0.1 Ohm is at rest in a horizontal plane. A uniform magnetic field 60 o away from the vertical increases from 0.5 T to 1.5 T in 0.60 s. a) What is the induced current in the loop? (LC) b) What is the direction of the current looking down from the vertical (CW or CCW)? (LC)