I Magnetic dipole and a torque

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The discussion centers on confusion regarding the magnetic torque formula, specifically the use of the sine function in relation to the angle between the magnetic dipole and the magnetic field. The participant questions why torque is calculated using an angle when the forces acting on a rectangular current loop are parallel and have no angle between them. Clarification is sought on the relationship between the magnetic dipole moment and the magnetic field in generating torque. The mention of the Lorentz force equation is suggested as a helpful reference for understanding the concept. Overall, the discussion highlights the complexities of magnetic torque in the context of current loops and magnetic fields.
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In reading chapter 6.1.2 I stumbled upon a magnetic torque concept which I don't understand, here is the problematic fragment
magnetic_dipole_torque.png


In the formula for N author multiplies by ##sin(\theta)## but why? The torque is said to be caused by forces (caused by magnetic field) on opposite side of a rectangular current loop. So there is no angle between them! They both lie in the same plane and are parallel to each other. IOW, the angle between is 0.
From the figure 6.2 it look like author takes an angle between m (magnetic dipole) and B (magnetic filed) but why if the torque is said to be generated by forces on opposite side of a rectangle?
 
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Hi,

Here you find a comprehensive picture, with the accompanying text you should be able to answer your question.

Personally I find it instructive to fall back on the equation for the Lorentz force.

##\ ##
 

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