A charged particle with charge $q$ and mass ' $m$ ' is moving with velocity $160 \mathrm{~ms}^{-1}$ in the region of magnetic field $\mathrm{B}$ at an angle $60^{\circ}$ with the direction of $\overrightarrow{\mathrm{B}}$. The pitch of helix formed by particle will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{160 \pi m}{q B} \)
Given,
B = magnetic field
q = charge
v, velocity = 160 m/s
θ, Angle between $\vec B$ and $\vec v$ = 60°$
Pitch (P) = $\frac{2\pi mv\cos\theta}{qB} = \frac{2\pi m\times 160\times \cos 60°}{qB}$
$=\frac{2\pi m\times 160\times \frac{1}{2}}{qB}$ $[\cos 60°=\frac{1}{2}]$
$= \frac{160\pi m}{qB}$