Q 12-04-194JEE MainJEE Main 2020 (3 Sep, Shift 1)Easy
A charged particle carrying charge $1\ \mu\text{C}$ is moving with velocity $(2\hat i + 3\hat j + 4\hat k)\ \text{m s}^{-1}$. If an external magnetic field of $(5\hat i + 3\hat j - 6\hat k)\times10^{-3}\ \text{T}$ exists in the region where the particle is moving then the force on the particle is $\vec F\times10^{-9}\ \text{N}$. The vector $\vec F$ is:
Answer: (B) $-30\hat i + 32\hat j - 9\hat k$
$$\vec v\times\vec B = \begin{vmatrix}\hat i & \hat j & \hat k\\ 2 & 3 & 4\\ 5 & 3 & -6\end{vmatrix}\times10^{-3} = (-30\hat i + 32\hat j - 9\hat k)\times10^{-3}$$
$\vec F_{mag} = q\,\vec v\times\vec B = 10^{-6}\times(-30\hat i + 32\hat j - 9\hat k)\times10^{-3} = (-30\hat i + 32\hat j - 9\hat k)\times10^{-9}$ N.
Solution by Sreeraj P, M.Sc Physics