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Electromagnetic Damping Time Constant

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A conducting rod of mass m and length L is placed on two frictionless, parallel conducting rails separated by a distance L. The rails are connected by a resistor R to form a closed circuit. A uniform magnetic field B is directed perpendicular to the plane of the circuit. If the rod is given an initial velocity v0v_0, what is the time required for the rod’s speed to decrease to v0/ev_0/e?

A

mR/B^2L

B

mR/B^2L^2

C

mR/BL

D

mR^2/B^2L^2

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