A horizontal wire is hung from the ceiling of a room by two massless strings. Th

Question

A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.21 m and a mass of 0.005 kg. A uniform magnetic field of magnitude 0.070 T is directed from the ceiling to the floor. When a current of I = 39 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle f with respect to the vertical, as the drawing shows. Find (a) the angle and (b) the tension in each of the two strings.

im pretty sure tension is not equal to mg, because there are both x and y components, this is where i am confused.

Explanation / Answer

The horizontal force on the wire F = ilB = (39 A)(0.21 m)(0.07 T) = 0.5733 N.

The vertical force is the weight, mg = (0.005 kg)(9.81 m/s2) = 0.04905 N.

There is no diagram, but the wire must be pushed sideways almost to the horizontal position. The tension must equal the negative of the vector sum of the two force vectors:

(0.57332 + 0.049052)½ = 0.5754 N and since the tension is shared between the two strings, the answer to part (b) is 0.2877 N.

The answer to part (a) is the arctangent (0.5733/0.04905) = 85.1°

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