In this situation, there are three long straight parallel wires, one passing thr

Question

In this situation, there are three long straight parallel wires, one passing through each corner of an equilateral triangle. A red current is out of the page, while a blue current is into the page. We're looking at a cross-sectional slice through the wires, seeing them end on. The arrow on each of the wires represents the net force that wire experiences because of its interactions with the other two wires we're assuming the only forces come from the magnetic interactions between the wires. Rank the wires, from largest to smallest, based on the magnitude of the current in each wire. Express your answer in the form 1>2-3 (use only> and/or signs).

Explanation / Answer

3>2>1

Force between 1 and 2 are attractive. Force between 1 and 3 is repulsive. Force between 2 and 3 is repulsive.

Looking at the blue wire(3) , if the currents in wire 1 and 2 were equal, the resultant force would have been straight on top. However, from the diagram the resultant force is tilted slightly to the left. This indicates that the force exerted by 2 on 3 is stronger than the the force exerted by 1 on 3. Since the distance bwteen 1 and 3 is same as distance between 2 and 3, the current in 2 has to be greater than 1. So current in 2 > 1.

In the same way, looking at 2, if the currents in wire 1 and 3 were equal, the resultant force would have been along the angular bisector of the exterior angle at 2 i.e, the resultant would have made an angle of 60 degrees with the base of the equilateral triangle.However, from the diagram the resultant force makes an angle > 60 degree. This indicates that the force exerted by 3 on 2 is stronger than the the force exerted by 1 on 2. Since the distance bwteen 1 and 3 is same as distance between 2 and 3, the current in 2 has to be greater than 1. So current in 3 > 1.

In the same way, looking at 1, if the currents in wire 3 and 2 were equal, the resultant force would have been along the angular bisector of the exterior angle at 1 i.e, the resultant would have made an angle of 60 degrees with the base of the equilateral triangle. However, from the diagram the resultant force makes an angle > 60 degree. This indicates that the force exerted by 3 on 1 is stronger than the the force exerted by 2 on 1. Since the distance bwteen 1 and 3 is same as distance between 1 and 2, the current in 3 has to be greater than 2. So current in 3 > 2.

So from the above 3 steps we get , 3>2, 3>1 and 2>1. Combining all 3 we get 3>2>1

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