Write the magnetic force equation on a current-carrying element $I\vec{dl}$ inside a magnetic field $\vec{B}$. Write the law used to determine the direction of the magnetic force.

(N/A) The magnetic force $d\vec{F}$ on a current-carrying element $I\vec{dl}$ placed in a magnetic field $\vec{B}$ is given by the vector product:
$d\vec{F} = I(d\vec{l} \times \vec{B})$
where $I$ is the current,$d\vec{l}$ is the infinitesimal length vector of the conductor,and $\vec{B}$ is the external magnetic field.
The direction of the magnetic force is determined by the Fleming's Left-Hand Rule.
According to this rule,if we stretch the thumb,forefinger,and middle finger of the left hand such that they are mutually perpendicular to each other,then:
$1$. The forefinger points in the direction of the magnetic field $(\vec{B})$.
$2$. The middle finger points in the direction of the current $(I)$.
$3$. The thumb will point in the direction of the magnetic force $(d\vec{F})$ acting on the conductor.