This simulation shows a current loop in uniform magnetic field.
The black arrows show the force due to magnetic field on the loop.
$\vec{F}= q \vec{v} \times \vec{B}$ or $\vec{F}= I \int d\vec{\ell} \times \vec{B}$
The magnetic field in in the +Z direction if Bz>0.
Then ,torque for the loop is calculated from definition $\vec{\tau}=\vec{r}\times\vec{F}$

Because the current flow in the same counter-clockwise direction.
The force on the loop change sign during each helf cycle.
If we current reverse direction during each helf cycle, the following device can turn into a motor.
A voltage source is needed in the loop to drive the current.
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P.S. The above simulation did not include the induced emf due to changing magnetic field in the loop.

You are welcomed to check out a very good animation [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1396.0]DC motor operation principle[/url]

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