You are looking head-on at a wire carrying a current. The wire is stretched so t

Question

You are looking head-on at a wire carrying a current. The wire is stretched so that the current is coming directly at you, out of the page. It is shown as a dot on the screen or page. The wire is in a uniform horizontal magnetic field shown as horizontal lines. The direction of the magnetic field is not shown in the figure. Choose and show the direction by drawing arrowheads on the lines, so that the wire can remain where it is, levitated, without crashing to the ground. The wire is carrying a current of 2.00 A and has a linear mass density of 2.50 x 104 kg/m. Find the magnitude of the magnetic field which will keep the wire levitated. Don’t forget to explain your diagram and your work.

Explanation / Answer

The B field has to go from left to right as you are looking at it; that way F = iL × B will be upwards.

The magnetic force has to support the weight, which for one meter of wire is (2.5 * 10-4 kg)(9.81 m/s2) = 2.45 * 10-3 N.

Since F = iLB, solve for B, get B = F/iL

= (2.45 * 10-3 N)/(2.00 A)(1.00 m) = 1.225 * 10-3 T

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