You have a cylindrical log of radius r and length l. It rests on a ramp that mak

Question

You have a cylindrical log of radius r and length l. It rests on a ramp that makes an angle with the horizontal. The reason the log does not roll down the ramp is as follows. There is a wire wrapped around the log in such a way that the plane of the wire loop is horizontal and it contains the axis of the log. Futhermore, the wire has a current i running through it, and there is a uniform magnetic field B-vector that runs perpendicular to the plane of the ramp. Show that the linear weight density (weight per unit length of log) is given by ?w = 2iB.

Explanation / Answer

Area of loop = 2rl

Force from magnetic field on loop = 2rlBi

Weight of log = ?lr

2rlBi = ?lr

therefore ? = 2iB

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