First slide

Force on a charged particle moving in a magnetic field

Question

A charged particle, carrying a charge Q moves with velocity 2 m/s in x-y plane in a uniform magnetic field $\vec{B} = (\hat{i} + 2 \hat{j} + 3 \hat{k}) T .$ Then magnitude of component of magnetic force experienced by the particle is zero

Moderate

Solution

$\vec{v} = a \hat{i} + b \hat{j}$ (a and b are non-zero quantities).
$∴ {\vec{F}}_{B} = \vec{Qv} \times \vec{B} = Q |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ a & b & 0 \\ 1 & 2 & 3 \end{matrix}| = Q [3 b \hat{i} - 3 a \hat{j} + (2 a - b) \hat{k}]$

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