Physics question? How did he get this answer? Any help is appreciated?

Question

What is the net force on the rectangular loop of wire that is 2.00 cm wide, 6.00 cm long and is located 2.00 cm from a long, straight wire that carries i= 40.0. A current as shown in the picture. Assume a current of 20.0 A is in the loop.

the answer is 1.5 x 10 ^-3 N

the answer is 1.5 x 10 ^-3 N

Steve4Physics · Accepted Answer

I don't agree with your answer.  But this is my solution.
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The field at the left side of the the loop is B = μ₀I/(2πr)
= 4π x10^-7 x 40.0/(2π x 0.02) = 4x10^-4 T

The force on the left side of the loop is F = BIL
= 4x10^-4 x 20.0 x 0.06
= 4.8 x 10^-4 N

As the current in the long wire is in the same direction as the current in the left side of the loop, this is a force of attraction.
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The field at the right left side of the the loop is B = μ₀I/(2πr)
= 4π x10^-7 x 40.0/(2π x 0.04) = 2x10^-4 T

The force on the left side of the loop is F = BIL
= 2x10^-4 x 20.0 x 0.06
= 2.4 x 10^-4 N

As the current in the long wire is in the opposite direction to the curretn in the right side of the loop, this is a force of repulsion.
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The top and bottom parts of the loop are perpendicular to the long wire and no force is exerted on them.
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The total force on the loop is therefore 4.8x10^-4 - 2.4x10^-4 = 2.4x10^-4N  directed  towards the long wire (to the left).

Physics question? How did he get this answer? Any help is appreciated?

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