How Does Current Direction Affect Force in a Rectangular Loop?

[ahazen]

A rectanglular loop consists of 5 turns of wire carrying a current of 2.8 A. The loop is in the x-y plane, and the direction of flow of the current is shown in the figure. The loop has dimensions a = 4 cm and b = 5 cm. Consider a uniform magnetic field of strength 3.8 × 10-4 T in x, y, or z directions.

I need to find the:
-Fa on x-axis
-Fb on y-axis
-Fa on z-axis
-Fb on z-axis

For the X-axis, I found that torque is 1.064e-5 and Fb=0
For the y-axis, I found the torque is 1.064e-5 and Fa=0
I also found that the torque for z-axis is 0.

But, how do I find the other Fa and Fb?
I am given: F=I*L*B sin(theta)

 

[alphysicist]

Hi ahazen,

A rectanglular loop consists of 5 turns of wire carrying a current of 2.8 A. The loop is in the x-y plane, and the direction of flow of the current is shown in the figure. The loop has dimensions a = 4 cm and b = 5 cm. Consider a uniform magnetic field of strength 3.8 × 10-4 T in x, y, or z directions.

I need to find the:
-Fa on x-axis
-Fb on y-axis
-Fa on z-axis
-Fb on z-axis

For the X-axis, I found that torque is 1.064e-5 and Fb=0
For the y-axis, I found the torque is 1.064e-5 and Fa=0
I also found that the torque for z-axis is 0.

But, how do I find the other Fa and Fb?
I am given: F=I*L*B sin(theta)

By Fa, I assume you mean the magnitude of the magnetic force on side a due to the magnetic field, right? If so, then you have the formula; if you plug in your values (all you have to determine here is what theta is) what do you get?

 

[ahazen]

yes, that's correct:) I'm still trying to work on the problem. Something is not working right when I plug the values in.

 

[alphysicist]

yes, that's correct:) I'm still trying to work on the problem. Something is not working right when I plug the values in.

You seem to have the right formula; if you post the values you are plugging in and the result you get, I or someone else can try to verify it.

 

[rwisz]

I can help you find the other Fa and Fb values for the rectangular loop by using the formula F=I*L*B sin(theta). First, let's define the variables in this formula.

F represents the force on the loop, I is the current in the wire, L is the length of the loop, B is the magnetic field strength, and theta is the angle between the direction of the current and the magnetic field.

For the Fa on the z-axis, we can use the same formula but with a different angle. Since the loop is in the x-y plane, the angle between the current and the magnetic field on the z-axis is 90 degrees. This means that the sin(theta) term will be equal to 1, so the formula becomes F=I*L*B.

To find Fa on the x-axis and Fb on the y-axis, we need to consider the direction of the current and the magnetic field. On the x-axis, the current is flowing in the positive direction and the magnetic field is also in the positive direction. This means that the angle between them is 0 degrees, so the sin(theta) term will be equal to 0 and the force will be 0.

On the y-axis, the current is flowing in the positive direction while the magnetic field is in the negative direction. This creates an angle of 180 degrees between them, so the sin(theta) term will be -1 and the formula becomes F=-I*L*B.

Using these formulas, we can find the Fa on the x-axis and Fb on the y-axis by plugging in the given values for I, L, and B.

I hope this helps you find the other Fa and Fb values for the rectangular loop. It's important to consider the direction and angle between the current and the magnetic field when using the formula for force. Keep in mind that the direction of the force will depend on the direction of the current and the magnetic field.