Uniform electric field E and magnetic field B, respectively, are along y-axis as shown in the figure. A particle with specific charge q/m leaves the origin O in the direction of x-axis with an initial non-relativistic speed `v_(0). The coordinate `Y_(n)` of the particle when it crosses the y-axis for the nth time is:

Options

A. `tan^(-1)((3v_(0)B)/(2pinE))`
B. `tan^(-1)((v_(0)B)/(pi nE))`
C. `tan^(-1)((v_(0)B)/(sqrt(2)pi nE))`
D. `tan^(-1)((v_(0)B)/(2pi nE))`

Answer

D

Explanation

As `v_(y)=a_(y)t=((qE)/m)((2pimn)/(qB))=(2pinE)/B`
Thus `tan alpha=(v_(0))/(v_(y))=(v_(0)B)/(2pinE)implies alpha=tan^(-1)((v_(0)B)/(2pin E))`