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CHarmon

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A DC motor contains a split ring commutator that reverses the direction of the current every 180 degrees which reverses the force direction, allowing constant directional torque and rotation.

Recall that F=nBILsin(θ), meaning torque is greatest when the coil is perpendicular to the magnetic field (θ=90).

In both parallel and radial magnets (usually what DC motors have), the magnetic field is always perpendicular to the coil, resulting in a constant force on the coil.

i.e F=nBILsin(90),
F=nBIL(1)
F=nBIL
 
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Hi there! All of the factors that counter into the magnitude of the force acting don't the coil remain constant. Like @CHarmon pointed out, this is F= BIl. Magnetic field is produced from them stationary magnets (constant), current is sourced from the power supply (constant) and length of the side in question is always the same.

Hence, force is constant!

Hope this helps :)
 

wizzkids

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Ignore all the conversation about commutators and radial magnetic fields.
Just consider a single current loop in a uniform B-field as shown below:
Untitled.png
The vertical segments are experiencing a constant force shown by the red vectors, and the two forces constitute a couple or moment. The horizontal segments are experiencing a variable force but these forces do not constitute a couple so they do not cause rotation.
The torque applied to the axis of the motor varies according to the cosine function where θ is the angle between the plane of the coil and the magnetic B-field vector
 

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