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HW #11 - Fields and Waves

# HW #11 - Fields and Waves - MasteringPhysics Assignment...

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MasteringPhysics: Assignment Print View Introduction to Faraday's Law Learning Goal: To understand the terms in Faraday's law for magnetic induction of electric fields, and contrast these fields with those produced by static charges. Faraday's law describes how electric fields and electromotive forces are generated from changing magnetic fields. It relates the line integral of the electric field around a closed loop to the change in the total magnetic field integral across a surface bounded by that loop: , where is the line integral of the electric field, and the magnetic flux is given by , where is the angle between the magnetic field and the local normal to the surface bounded by the closed loop. Direction : The line integral and surface integral reverse their signs if the reference direction of or is reversed. The right-hand rule applies here: If the thumb of your right hand points along http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1046285 (1 of 27)5/5/2006 10:32:51 PM

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MasteringPhysics: Assignment Print View , then the fingers point along . You are free to take the loop anywhere you choose, although usually it makes sense to choose it to lie along the path of the circuit you are considering. Part A Consider the direction of the electric field in the figure. Assume that the magnetic field points upward, as shown. Under what circumstances is the direction of the electric field shown in the figure correct? Hint A.1 Hint not displayed ANSWER: always if increases with time if decreases with time depending on whether your right thumb is pointing up or down Part B Now consider the magnetic flux through a surface bounded by the loop. Which of the following statements about this surface must be true if you want to use Faraday's law to relate the magnetic flux to the line integral of the electric field around the loop? ANSWER: The surface must be the circular disk in the middle of the loop. The surface must be perpendicular to the magnetic field at each point. The surface can be any surface whose edge is the loop. The surface can be any surface whose edge is the loop as long as no magnetic field line passes through it more than once. You are free to take any surface bounded by the loop as the surface over which to evaluate the integral. The result will always be the same, owing to the continuity of magnetic field lines (they never start or end anywhere, since there are no magnetic charges). It is important to understand the vast differences between electric fields produced by changing magnetic fields via Faraday's law and the more familiar electric fields produced by charges via Coulomb's law. Here are some short questions that illustrate these differences. Part C http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1046285 (2 of 27)5/5/2006 10:32:51 PM
MasteringPhysics: Assignment Print View When can an electric field be measured at any point from the force on a stationary test charge at that point?

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