Question

Consider the motion of a positive point charge in a region where there are simultanceous uniform electric and magnetic fields $\overrightarrow{E}=E_0\hat{j}$ and $\overrightarrow{B}=B_{)}\hat{j}$. At time $t=0$, this charge has velocity $\overrightarrow{v}$ in the $x-y$ plane, making an angle $\theta$ with the $x$-axis. Which of the following option(s) is/are correct for time $t>0$?

• A. If $\theta =0^o$, the charge undergoes helical motion with contant pitch along the $y$-axis
• B. If $\theta =0^o$, the charge moves in a circular path in the $x-z$ lane
• C. If $\theta ={90}^o$, the charge undergoes linear but accelerated motion along the $y$-axis
• D. If $\theta ={10}^o$, the charge undergoes helical motion with its pitch increasing with time, along the $y$-axis

Answer 1

Answer: (C), (D)

If $\theta ={10}^o$, the charge undergoes helical motion with its pitch increasing with time, along the $y$-axis

For $\theta ={10}^o$, path is helical.
Since there is an electric field, pitch is increasing
For $\theta ={90}^o$, path is stright line as $\overrightarrow{B}$ will not exert any force.