Why Does Torque Change in a Rotating Coil Even if the Force Remains Constant?

[delsoo]

Homework Statement

for this question, since area of cutting of magnetic field change, so magnetic flux change, f is unchanged . but i don't understand why the torque will change since the force is unchanged, since torque=FORCE X DISTANCE FROM THE ROTATING PIVOT

Homework Equations

The Attempt at a Solution

 

[dauto]

Distance between the line of action of the force and the pivot is changing.

 

[delsoo]

Can you explain.further. I can't see and understand the situation.

 

[TSny]

but i don't understand why the torque will change since the force is unchanged, since torque=FORCE X DISTANCE FROM THE ROTATING PIVOT

Careful. Torque is generally not equal to the product of the force, F, and the distance, r, between the axis of rotation and the point of application of the force. As dauto is pointing out, torque is the product of force and "lever arm", d.

 

[HalfLostAndSearching]

The torque of a rotating coil is a result of the interaction between the magnetic field and the current flowing through the coil. It is given by the equation T = NIABsin(theta), where N is the number of turns in the coil, I is the current, A is the area of the coil, B is the magnetic field strength, and theta is the angle between the magnetic field and the normal to the coil.

In this scenario, the magnetic flux is unchanged because the area of cutting of the magnetic field is unchanged. However, the torque can still change because the angle theta can change. This can happen if the coil is not perfectly perpendicular to the magnetic field, or if the coil is rotating around an axis that is not aligned with the magnetic field. In these cases, the distance from the rotating pivot to the point where the force is applied (the center of the coil) will change, resulting in a change in the torque.

Additionally, the torque can also change if the current or the magnetic field strength changes. If the current increases, the torque will increase as well, and if the magnetic field strength increases, the torque will decrease. This is because both of these variables are directly proportional to the torque in the equation.

Therefore, even though the force may remain unchanged, the torque can still change due to changes in the angle theta, the current, or the magnetic field strength.