An electron is travelling along the x-direction. It encounters magnetic field in the y-direction. Its subsequent motion will be

Options

A. straight line along the xz-direction
B. a circle in the xz-plane
C. a circle in the yz-plane
D. a circle in the xy-plane

Answer

D

Explanation

If a particle carrying q and moving with elocity v through a point in magnetic field experiences a deflecting force F, then magnetic fieled `vec(B)` is given by

`vec(F)=qvecvxxvecB`
`"Here" vecv=v_(x) hati and `
`vecB=B_(y)hatj`
`therefore vecF=ev_(x) B_(y) (hatixxhatj)=ev_xB_(y)hatk`
Hence subsequent motion of the charged particle will be a circle in hte xy-plane.