How to Calculate the Net Force on a Rectangular Loop by a Straight Wire?

[physics213]

Homework Statement

In the figure below, the current in the long, straight wire is I1 = 4.8 A, and the wire lies in the plane of the rectangular loop, which carries 9.7 A. The dimensions shown are c = 0.10 m, a = 0.15 m, and l = 0.45 m. Find the magnitude and direction of the net force exerted by the magnetic field due to the straight wire on the loop.

Homework Equations

F/l = (1.26E-6)(I1)(I2)/(2)(pi)(d)

F= IlBsin(theta)

B=(1.26E-6)(I)/(2)(pi)(r)

The Attempt at a Solution

I figured that we would have to use a combination of the three equations above, and I got an answer of 4.2E-5, but this is incorrect. I believe this answer only takes into account the two wires, not the wire and the rectangle. I am not really sure how to take into account the rectangle. Please help!

 

[rl.bhat]

Sides of the rectangle parallel to the wire will experience opposite forces. Find the resultant to get the net force.

 

[nlightner]

I would suggest approaching this problem by first drawing a diagram and labeling all the variables given in the problem. This can help to visualize the situation and identify any missing information.

Next, I would recommend breaking down the problem into smaller parts. Start by finding the magnetic field created by the long, straight wire at the location of the rectangular loop. This can be done using the equation B=(1.26E-6)(I)/(2)(pi)(r), where r is the distance from the wire to the loop.

Once the magnetic field is determined, you can use the equation F= IlBsin(theta) to find the force exerted on each segment of the rectangular loop. Keep in mind that the force will have both a magnitude and direction, so you may need to use vector addition to find the net force on the loop.

Finally, you can use the equation F/l = (1.26E-6)(I1)(I2)/(2)(pi)(d) to check your answer. This equation represents the force per unit length between two parallel current-carrying wires, where d is the distance between the wires. In this case, you can use this equation to find the force per unit length between the straight wire and one side of the rectangle, and then multiply by the length of the side to find the total force on that side. Repeat this for each side of the rectangle and then add all the forces together to find the net force on the loop.

Remember to pay attention to the direction of the forces and use proper units in your calculations. If you are still having trouble, I would recommend seeking assistance from a teacher or tutor to clarify any misunderstandings and guide you through the problem step by step.