Question

A charged particle moves with a constant velocity $(\hat{i}+\hat{j})m/s$ in a magnetic field $\overrightarrow{B}=(2\hat{i}+3\hat{k})$ and uniform electric field $\overrightarrow{E}=(a\hat{i}+b\hat{j}+c\hat{k})N/C$ , then $($assuming all quantities in S.I. unit$):$

• A. $a=-3$
• B. $b=3$
• C. $c=-2$
• D. $a^2+b^2+c^2=22$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $a=-3$
B $b=3$
D $a^2+b^2+c^2=22$

Since the charge particle is moving with constant velocity, its acceleration will be 0.

$F_{net}=0$

$F_{el}+F_{mag}=0$

In equilibrium, electric force $=$ - magnetic force

So, $q\overrightarrow{E}=-q(\overrightarrow{v}\times \overrightarrow{B})$ or $a\hat{i}+b\hat{j}+c\hat{k}=-(3\hat{i}-3\hat{j}-2\hat{k})$

So, $a=-3,b=3,c=2$and $a^2+b^2+c^2=9+9+4=22$