Force On A Moving Charge In Magnetic Field - Practice Questions & MCQ

Force on a moving charge in magnetic field: 

The magnetic force  on a free moving charge is perpendicular to both the velocity of the charge and the magnetic field with direction given by the right hand rule. The force is given by the charge times the vector product  of velocity and magnetic field.

The force is always perpendicular to both the magnetic field and velocity.

$
\begin{aligned}
& F=q v B \sin \theta \\
& F=q v B \text { if } \theta=90
\end{aligned}
$

If the velocity is perpendicular to the magnetic field then the force is given by the simple product :

$
\text { Force }=\text { charge } \times \text { velocity } \times \text { B-field }
$

Right hand rule: speed $v$ in a magnetic field of strength $B$ is given by

$
F=q v B \sin \theta,
$

the tesla ( T ). Therefore magnetic field strength is given as :

$
B=\frac{F}{q v \sin \theta}
$
 

The unit of tesla is :

$
1 \mathrm{~T}=\frac{1 \mathrm{~N}}{\mathrm{C} \cdot \mathrm{~m} / \mathrm{s}}=\frac{1 \mathrm{~N}}{\mathrm{~A} \cdot \mathrm{~m}}
$

- The direction of the force on a moving charge is given by right hand rule. Point the thumb of the right hand in the direction of $v$, the fingers in the direction of $B$, and a perpendicular to the palm points in the direction of $F$.
- The force is perpendicular to the plane formed by $\boldsymbol{v}$ and $\boldsymbol{B}$. Since the force is zero if $\boldsymbol{v}$ is parallel to $\boldsymbol{B}$, charged particles often follow magnetic field lines rather than cross them.