Quiz1 - z< exerts on the piece at z> 0(30 points 3 a...

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Physics 3123 (Spring 2011), 1 st Quiz 3/4/11 1. A straight wire that coincides with the x -axis of a cartesian coordinate system carries current I. A conducting, rectangular loop with sides a ( || ˆ x ) and b ( || ˆ y ) moves with velocity vV = V ˆ y away from the wire. The loop has resistance R and it starts its motion at time t = 0 at a distance 3 b from the wire (measured from the center of the loop to the wire). Compute the current I loop induced in the loop as a function of time. (30 points) 2. A hollow, cylindrical conductor (radius R ) whose axis coincides with the x -axis of a cartesian coordinate system carries a surface charge density σ . The conductor is assembled from two pieces that meet in the xy -plane. Compute the force per unit length that the piece of the conductor at
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Unformatted text preview: z < exerts on the piece at z > 0. (30 points) 3. a) Derive a wave equation from Maxwell’s equations and Fnd the corre-sponding wave velocity. (Hint: take the curl of the third and the fourth one of Maxwell’s equations.) (15 points) b) ±ind monochromatic plane waves that solve Maxwell’s equations. (10 points) c) A wave as you found them in b) hits a spherical black body (radius R ), that is an object that absorbs all radiation that falls onto it. How much energy and momentum does the wave transfer to the black body in a time interval Δ t ? Which direction does the resulting force have? (15 points) 1...
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