Find the magnitude of the net force exerted on the loop by the magnetic field created by the long wire. Answer in units of N.

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A current in the long, straight wire, which lies in the plane of rectangular loop, that also carries a current, as shown in the figure.

Find the magnitude of the net force exerted on the loop by the magnetic field created by the long wire. Answer in units of N.

Net Force = N

Explanation: Force and Magnetic field are related through the following formula:

F = I.L.B.sinθ

Magnetic field (B) in a straight long wire is given by

in which

is permeability of free space and is T.m/A

I is current in the wire;

r is distance to the wire;

Examining the square loop and using the right hand rule, the top, which we will name it F₂, and the bottom, named F₄, have angle θ = 0, giving sin(0) = 0 and therefore, F₁ = F₃ = 0.

So, for the net force, the relevant forces will be on the sides parallel to the wire.

For the other forces, angle is 90°, sin(90°) = 1, then:

F = I.L.B

Replacing magnetic field:

F =

Note: The side closest to the wire is F₁, while the farthest is F₃.

Note2: As the constant unit is in meters, distance and length of side of the square loop are also in meters.

Calculating forces:

F₁ =

F₁ = N

Current in F₃ is flowing thoruhg the negative side of the referential, so:

F₃ =

F₃ = N

Net force is total force:

The total force acting on the square loop is N.

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