You need to add dollar sign for those equations.
Otherwise, those equation would not be convert to image.

The following is what you have copied.
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.