Magnetic Force on segment of wire

[Aerospace]

A segment of wire carries a current of 30 A along the x-axis from x=-6m to x=0 and then along the z axis from z=0 to z=5.5m. In this region of space, the magnetic field is equal to 14mT in the positive z direction. What is the magnitude F of the force on the segment of wire? Answer in units of N.

I'm not sure what formula to use, can anyone help?

 

[Doc Al]

Originally posted by Aerospace
I'm not sure what formula to use, can anyone help?

The magnetic force on a segment of current-carrying wire is:
$$F = i\vec{l} \times \vec{B}$$

 

[M98Ranger]

To calculate the magnetic force on the segment of wire, we can use the formula F = I * L * B * sin(theta), where I is the current, L is the length of the wire, B is the magnetic field, and theta is the angle between the wire and the magnetic field.

In this case, we can break up the segment of wire into two parts: one along the x-axis and one along the z-axis. The force on each part will be in a different direction, so we need to calculate them separately.

For the segment along the x-axis, the length L = 6m and the angle between the wire and the magnetic field is 90 degrees, so sin(theta) = 1. Plugging in the values, we get F = (30 A) * (6m) * (14 mT) * (1) = 2520 N.

For the segment along the z-axis, the length L = 5.5m and the angle between the wire and the magnetic field is 0 degrees, so sin(theta) = 0. Plugging in the values, we get F = (30 A) * (5.5m) * (14 mT) * (0) = 0 N.

Therefore, the total force on the segment of wire is 2520 N.