Calculating Force on Rectangular Loop from Straight Wire

[Fisicks]

Homework Statement

A rectangular loop of wire is placed next to a straight wire. There is a current of 3.5 A in both wires. Determine the direction and magnitude of the net force on the loop.

Homework Equations

F=BIL

The Attempt at a Solution

I am kinda confused here. Will the rectangular loop feel a force without the straight wire? The current will create a magnetic field inside the loop. Is this field constant everywhere? If so then i believe the forces cancel. Then you just have to find the force on the two vertical sides of the rectangular loop caused by the straight wire.

 

[da_nang]

Homework Statement

A rectangular loop of wire is placed next to a straight wire. There is a current of 3.5 A in both wires. Determine the direction and magnitude of the net force on the loop.

Homework Equations

F=BIL

The Attempt at a Solution

I am kinda confused here. Will the rectangular loop feel a force without the straight wire? The current will create a magnetic field inside the loop. Is this field constant everywhere? If so then i believe the forces cancel. Then you just have to find the force on the two vertical sides of the rectangular loop caused by the straight wire.

I do believe the net force acting on the loop caused by its own magnetic field will cancel each other. Using the right hand rule, with the current coing counter-clockwise and looking straight down on it, the magnetic field inside will pointing out of the page, the field outside the loop will point into the page. It won't be uniform due to Biot-Savart's law. However, if one side of the loop is affected by one magnetic force, then the opposite will be affected by an equal but opposite force since they're parallell. The magnetic field produced by the one wire affects the opposite wire by a magnetic force directed out of the loop, and the opposite wire produces it's own magnetic field to affect the other wire with the same force in the other direction. Thus the internal magnetic field of the loop yields zero net force.

To then find the net force acting on the loop caused by the straight wire would depend on the where the straight wire is and the direction of the current in the wire. If the wire's parallell to one side, using the formula for the magnetic force between two parallell wires should yield a suitable answer. You then only need to consider the forces acting on the parallell sides of the loop, since the forces acting on the orthogonal sides would cancel each other out.