A loop of wire has the shape of a right triangle (see the drawing) and carries a

Question

A loop of wire has the shape of a right triangle (see the drawing) and carries a current of I = 3.90 A. A uniform magnetic field is directed parallel to side AB and has a magnitude of 2.20 T.

(a) Find the magnitude and direction of the magnetic force exerted on each side of the triangle.

(b) Determine the magnitude of the net force exerted on the triangle.
N

side AC     N directed  ---Select--- upwards downwards to the left to the right into the page out of the page (no force) side CB     N directed  ---Select--- upwards downwards to the left to the right into the page out of the page (no force) side BA     N directed  ---Select--- upwards downwards to the left to the right into the page out of the page (no force) A loop of wire has the shape of a right triangle (see the drawing) and carries a current of I = 3.90 A. A uniform magnetic field is directed parallel to side AB and has a magnitude of 2.20 T. (a) Find the magnitude and direction of the magnetic force exerted on each side of the triangle. side AC N directed ---Select--- upwards downwards to the left to the right into the page out of the page (no force) side CB N directed ---Select--- upwards downwards to the left to the right into the page out of the page (no force) side BA N directed ---Select--- upwards downwards to the left to the right into the page out of the page (no force) (b) Determine the magnitude of the net force exerted on the triangle. N

Explanation / Answer

For each side, F = IL X B, a vector cross product, and |F| = ILBsin?, where ? is the angle between IL and B.
To solve the problem, for each side use trig to get the length L and simple geometry to determine ?. Then plug the values into the equation.
Note ? = 0 for side AB so its force = 0. And the signs of the forces on AC and CB are opposite; one is into the page and one is out. I'll leave it to you to determine which is which; use the right-hand rule (ref.). And the magnitudes of the forces on AC and CB are equal (|BCsin?| = |AC|), so ... answer B = 0!

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