Question

An electric charge $+q$ moves with velocity $\overline{V}=3\hat{i}+4\hat{j}+\hat{k}$, in an electromagnetic field given by $\overline{E}=3\hat{i}+\hat{j}+\hat{2}k$ $\overline{B}=\hat{i}+\hat{j}+\hat{3}k$.The y-component of the force experienced by +q is:

• A. $-7q$
• B. $11q$
• C. $5q$
• D. $3q$

Answer 1

Answer: (A)

$-7q$

Given that,

Velocity, $v=(3\hat{i}+4\hat{j}+\hat{k})$

Electric field, $E=3\hat{i}+\hat{j}+2\hat{k}$

Magnetic field, $B=\hat{i}+\hat{j}+3\hat{k}$

Force,

$F=q(\text{E+v}\times \text{B})$

$F=q(3\hat{i}+\hat{j}+2\hat{k}+\left(\right(3\hat{i}+4\hat{j}+\hat{k})\times (\hat{i}+\hat{j}+3\hat{k}))$

$F=q(3\hat{i}+\hat{j}+2\hat{k}+11\hat{i}-8\hat{j}-\hat{k})$

$F=q(14\hat{i}-7\hat{j}+\hat{k})$

So, y-component of force experienced by +q is

$F_y=-7q$