Question

An electron enters an electric field having intensity $\overrightarrow{E}=3\hat{i}+6\hat{j}+2\hat{k}$ $V{m}^{-1}$ and magnetic field having induction $\overrightarrow{B}=2\hat{i}+3\hat{j}T$ with a velocity $\overrightarrow{V}=2\overrightarrow{i}+3\overrightarrow{j}$ ${ms}^{-1}$. The magnitude of the force acting on the electron is (Given $e=-1.6\times {10}^{-19}C$)

• A. $2.02\times {10}^{-18}N$
• B. $5.16\times {10}^{-16}N$
• C. $3.72\times {10}^{-17}N$
• D. $4.41\times {10}^{-18}N$
• E. None of the above

Answer 1

Answer: (E)

None of the above

The electric force acting on the electron is $qE=-e(3\hat{i}+6\hat{j}+2\hat{k})N$

The magnetic force acting on the electron=$q(\overrightarrow{v}\times \overrightarrow{B})$

$=q\left(\right(2\hat{i}+3\hat{j})\times (2\hat{i}+3\hat{j}\left)\right)$

$=0$

Hence net force acting on the electron is $-e(3\hat{i}+6\hat{j}+2\hat{k})$

Magnitude of this force=$e\left(\sqrt{3^2+6^2+2^2}\right)$

$=7e=11.2\times {10}^{-19}N$