Torque on a current loop about a hinge line

[theowne]

Homework Statement

A rectangular 20 turn loop that is 12 by 5 cm carries a current of 0.10A. It's hinged at one of the longer 12cm sides. It's mounted with its plane at an angle of 33 degrees to the direction of a magnetic field of 0.50T. What's the torque about the hinge line?

Homework Equations

T = iAbsin(theta)

The Attempt at a Solution

I guess my question is about the significance on the hinge line. The example in my book hinges on the z axis located in the middle of loop, so it uses the formula:

t = 2iaB (b/2) sin (theta)
where b/2 sin(theta) is decribed as the "moment arm". When it is hinged on the left longer side instead of the z axis, does this mean the equation would become 2iaB b sin (theta) instead?

 

[tiny-tim]

Hi theowne !

(have a theta: θ )

The example in my book hinges on the z axis located in the middle of loop, so it uses the formula:

t = 2iaB (b/2) sin (theta)
where b/2 sin(theta) is decribed as the "moment arm". When it is hinged on the left longer side instead of the z axis, does this mean the equation would become 2iaB b sin (theta) instead?

There's various ways of looking a this (including actually working it out from scratch ), but the easiest is probably to add a second loop next to the first, making one big loop with a hinge in the middle!

 

[kerimek]

The torque on a current loop about a hinge line is dependent on the orientation of the loop and the direction of the magnetic field. In this case, the loop is hinged on one of its longer sides and is mounted at an angle to the magnetic field. The torque can be calculated using the equation T = iAbsin(theta), where i is the current, A is the area of the loop, B is the magnetic field strength, and theta is the angle between the plane of the loop and the direction of the magnetic field. The moment arm, which is the distance between the hinge line and the line of action of the force, is bsin(theta) in this case. Therefore, the torque about the hinge line would be 2iaB bsin(theta). It is important to consider the location of the hinge line when calculating the torque on a current loop to accurately determine the direction and magnitude of the torque.