Question

A uniform magnetic field $\overrightarrow{B}=B_x\hat{i}+B_y\hat{j}+B_z\hat{k}$ and uniform electric field $\overrightarrow{E}=E_r\hat{i}+E_y\hat{j}+E_z\hat{k}$ exists in a space. A particle enters the region with initial velocity $\overrightarrow{u}=u_x\hat{i}+u_y\hat{j}+u_z\hat{k}$. If $\overrightarrow{u}\times \overrightarrow{B}=0$ and $\overrightarrow{u}\times \overrightarrow{E}=0$, the path of charged particle will be:

• A. Cricle
• B. Helix with uniform pitch
• C. Straight line
• D. Helix with variable pitch

Answer 1

The correct option is C Straight line

If $\overrightarrow{u}\times \overrightarrow{B}=0$, it means that velocity and magnetic field are parallel, or antiparallel $(\theta =0^{\circ }$ or $\pi$).

If $\overrightarrow{u}\times \overrightarrow{E}=0$, it means that velocity and electric field are parallel or antiparallel $(\theta =0^{\circ }$ or $\pi$)

Hence, we conclude that $\overrightarrow{u},\overrightarrow{E}$ and $\overrightarrow{B}$ will be in either same or opposite direction.

$\therefore$ Path of particle will be straight line as only electric force will act and $F_{magnetic}=0$

Hence, option$\left(c\right)$ is the correct answer.