A very simple application of magnetic forces can be used to make a nifty device

Question

A very simple application of magnetic forces can be used to make a nifty device called a "rail gun." These have been proposed as devices that could be used to send back to earth (or the moon) raw materials mined from an asteroid. The idea is shown in the figure below A bar of mass m can slide on two parallel rails separated by a distance H, and the whole apparatus is in a uniform magnetic field with magnitude D pointing into the plane of the paper. The rails are hooked up to a current source, and a current I passes through the rails and through the bar, which experiences a force that accelerates it down a track of length D. A bucket can be put on the bar, and anything in the bucket gets thrown off when the bar caches the end of the rail. Given the information above, determine the speed of the bar just before it reaches the end of the rails.

Explanation / Answer

Here , when a current I passes through the bar

magnetic force acting on the bar , F = B *I*H

Now, for the speed of bar

Using work energy theorum

0.5 * m * V^2 = F * D

0.5 * m * V^2 = B *I*H * D

solving for V

V = sqrt(2 * B*I*H*D/m)

where m is the mass of bar

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