What Orientation Produces Maximum Torque in a Magnetic Field?

[Inertialforce]

Homework Statement

The problem is as seen in the attachment.

Homework Equations

T(torque) = (N)(I)(A)(B)(Sin(theta))

The Attempt at a Solution

For this question I used the above formula to find the magnitude of the torque, but what I am not sure about is which orientation would produce the "maximum torque" that it is asking about.

Could someone please tell me which orientation would give a "maximum torque" and why?

By the way, I calculated the magnitude of the torque to be 18 Newton*meters.

 

[psykatic]

$$\theta$$ is the angle between the coil and the the direction of magnetic induction. or rather the direction of the current and the magnetic induction. Now try putting the values of $$\theta$$ accordingly and try and get the answer. By the way, what did you take the value theta to be, when you calculated its magnitude as 18Nm?

 

[thomate1]

I would like to clarify a few things about torque and magnetic fields before discussing the solution to this problem.

Torque is a rotational force that causes an object to rotate around an axis. It is measured in Newton-meters (Nm) and is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

In the context of magnetic fields, torque is the rotational force experienced by a magnetic dipole (a magnet or current-carrying wire) when placed in a magnetic field. It is calculated using the equation T = NIA sin(theta), where N is the number of turns in the wire, I is the current flowing through the wire, A is the area of the loop, and theta is the angle between the magnetic field and the plane of the loop.

Now, for the solution to this problem, we need to find the orientation that would produce the maximum torque. To do this, we need to understand the relationship between the magnetic field and the plane of the loop.

As per the right-hand rule, if you point your thumb in the direction of the current flow and curl your fingers, the direction in which your fingers curl will give you the direction of the magnetic field. In this case, the magnetic field is pointing towards the right side of the loop (out of the page).

Now, if we vary the angle theta between the magnetic field and the plane of the loop, we can see that the maximum torque will be produced when the angle is 90 degrees (perpendicular). This is because, at this angle, the magnetic field is acting on the loop with the maximum force, causing it to rotate with the maximum torque.

In contrast, when the angle is 0 or 180 degrees (parallel), the torque will be zero since there is no force acting on the loop.

Therefore, to answer the question, the orientation that would produce the maximum torque is when the magnetic field is perpendicular to the plane of the loop (90 degrees). This orientation is also known as the "maximum torque position."

I hope this helps to clarify any confusion and provides a clear understanding of the solution. Remember, as scientists, it is essential to understand the underlying principles and concepts before attempting to solve any problem.