The magnetic force acting on a charged particle of charge $-2 \mu \mathrm{C}$ in a magnetic field of $2…
The magnetic force acting on a charged particle of charge $-2 \mu \mathrm{C}$ in a magnetic field of $2 \mathrm{~T}$ acting in $y$ direction, when the particle velocity is $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}) \times 10^6 \mathrm{~ms}^{-1}$ is
$8 \mathrm{~N}$ in $-\mathrm{z}$ direction
$4 \mathrm{~N}$ in $z$ direction
$8 \mathrm{~N}$ in $y$ direction
$8 \mathrm{~N}$ in $z$ direction
Solution
Key Idea: When a charge q moves with velocity $\vec{v}$ inside magnetic field of strength $\overrightarrow{\mathrm{B}}$, then force on charge is called magnetic Lorentz force. The magnetic Lorentz force is in the direction of vector $\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}}$
$\begin{aligned}
& \text { Magnetic Lorentz force } \overrightarrow{\mathrm{F}}=q(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}}) \\
&=-2 \times 10^{-6}\left[2 \times 2 \times 10^6\right] \\
&=8 \mathrm{~N} \text { along negative -axis }
\end{aligned}$