Discussion Forum



1)

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


A) If $\theta=0^{0}$ the charge moves in a circular path in the x-z Plane

B) if $\theta=0^{0}$,the charge undergoes helical motion with constant pitch along the Y-axis

C) if $\theta=10^{0}$ the charges undergoes helical motion with its pitch increasing with time along the y-axis

D) if $\theta=90^{0}$ , the charge undergoes linear but accelerated motion along the y-axis

Answer:

Option C,D

Explanation:

(a) and (b)

 9112021563_k1.PNG

 

The magnetic field will rotate the particle in a circular path {in x-z plane or perpendicular to B). The electric field will exert a constant force on the particle in Positive y-direction. Therefore, the resultant path is neither purely circular nor helical or the options (a) and (b) both are wrong

 (c) 

9112021993_k2.PNG

$v_{\perp}$ and B will rotate the particle in a circular path in the x- z plane (or perpendicular to B). Further $v_{||}$ and E will move the panicle (with increasing speed) along the positive y-axis (or along the axis of the above circular path). Therefore, the resultant path is helical with increasing pitch, along the y-axis (or along B and E). Therefore option (c) is correct.
(d)

9112021277_k3.PNG

Magnetic force is zero, as $\theta$  between B and v is zero. But electric force will act in the y-direction. Therefore. motion is 1-D  and uniformly accelerated (towards positive y-direction).