Question

In a given region a charge particle is moving under the effect of electric and magnetic field with uniform velocity $\overrightarrow{v}=(\hat{i}+\hat{j}-\hat{k})$ m/s and magnetic field is given as $\overrightarrow{B}=(2\hat{i}+\hat{j}-2k)T$. The electric field is given as?

• A. $(i+j-k)$ V/m
• B. $(i-j+k)$ V/m
• C. $(i+k)$ V/m
• D. $(-i-k)$ V/m

Answer 1

The correct option is D $(-i-k)$ V/m

We know Force $F=qE$------(1)

and also $F=qV\times B$-----(2)

From 1 and 2 we get

$V\times B=E$

$V\times B$=$$\begin{array}{ccc}\hat{i}& \hat{j}& \hat{i}\\ 1& 1& -1\\ 2& 1& -2\end{array}$$

$V\times B=(-2+1)\hat{i}-(-2+2)\hat{j}+(1-2)\hat{k}$
$V\times B==-\hat{i}-\hat{k}$