Question

A certain region has an electric field $\vec{E}=(2\hat{i}-3\hat{j})N/C$ and a uniform magnetic field $\vec{B}=(5\hat{i}+3\hat{j}+4\hat{k})T$. The force experienced by a charge $1C$ moving with velocity $(\hat{i}+2\hat{j})m{s}^{-1}$ is

• A. $(10\hat{i}-7\hat{j}-7\hat{k})$
• B. $(10\hat{i}+7\hat{j}+7\hat{k})$
• C. $(-10\hat{i}+7\hat{j}+7\hat{k})$
• D. $(10\hat{i}+7\hat{j}-7\hat{k})$

Answer 1

Answer: (A)

Lorentz force, $\vec{F}=q\{\vec{E}+(\vec{v}\times \vec{B})\}$
$\vec{v}\times \vec{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 2& 0\\ 5& 3& 4\end{array}\right|=8\hat{i}-4\hat{j}-7\hat{k}$
$\vec{F}=1(2\hat{i}-3\hat{j}+8\hat{i}-4\hat{j}-7\hat{k})=(10\hat{i}-7\hat{j}-7\hat{k})$