A charged particle of specific charge `alpha` moves with a velocity `vecv=v_0hati` in a magnetic field `vecB=(B_0)/(sqrt2)(hatj+hatk)`. Then (specific charge=charge per unit mass)

Options

A. path of the particle is a helix
B. path of the particle is circle
C. distance moved by the particle in time `t=pi/(B_0alpha) is (piv_0)/(B_0 alpha)`
D. velocity of the particle after time `t=pi/(B_0alpha) is ((v_0)/2hatj+(v_0)/2hatj)`

Answer

(b,c)

Explanation

`vecVbotvecB`
Therefore, path of the particle is a circle. In magnetic field, speed
of the particle remains constant. Therefore, distance moved by
particle in time `t=pi/(B_0alpha) is v_0t or (piv_0)/(B_0alpha)`
Magnitude of velocity is always `v_0`, hence option (d) is incorrect.