Question

An electron moving with a velocity $V_1=2\hat{i}m/s$ at a point in a magnetic field experiences a force $\overrightarrow{F_1}=-2\hat{j}N$. If the electron is moving with a velocity $\overrightarrow{V_2}=2\hat{j}m/s$ at the same point, it experiences a force $\overrightarrow{F_2}=2\hat{i}N$. The force electron would experience if it were moving with a velocity $\overrightarrow{V_3}=2\hat{k}m/s$ at the same point is

• A. Zero
• B. $2\hat{k}N$
• C. $-2\hat{k}N$
• D. Information is insufficient

Answer 1

The correct option is A Zero

Let the magnetic field be $\overrightarrow{B}=B\hat{n}$
We have,
$\overrightarrow{F}=q(\overrightarrow{V}\times \overrightarrow{B})-2\hat{j}=(-e)(2\hat{i}\times B\hat{n})\Rightarrow \hat{j}=eB(\hat{i}\times \hat{n})\Rightarrow eB=1and\hat{n}=-\hat{k}(\because \hat{i}\times \hat{k}=\hat{j})\Rightarrow \overrightarrow{B}=\frac{1}{e}(-\hat{k})$

The information about $\overrightarrow{V_2}$ and $\overrightarrow{F_2}$ is redundant and it need not be considered. If considered, it will yeild the same answer as above.

If the electron moves with $\overrightarrow{V_3}=2\hat{k}$ if will be moving anti-parallel to $\overrightarrow{B}$. Thus it will not experience any force.