Slowing Down an Object with Magnetic Field

A rectangular conducting loop with mass m, resistance R, and an initial velocity (as shown in below figure) enters into a region with a uniform magnetic field B, which is perpendicular to the plane of the loop and pointing into the page as seen from the top. The side lengths of the loop are given as L and w. The width of the region with the magnetic field is also given as w.

a) Choose an appropriate coordinate axis and find the magnetic force acting on the loop throughout its motion. Using the equations of motion, find the speed as a function of time, and as a function of position. Then, find the position of the loop as a function of time.

b) Find the power delivered to the loop and the power dissipated through the loop (due to its resistance) at any given time.

c) How long does it take for the loop to leave the region with the magnetic field? What is the minimum value for w so that the loop can be stopped before it leaves the region?



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