Question

A particle carrying charge q enters a magnetic field B with velocity v at an angle
Θ≠0≠90° . Show that it follows a helical path. Determine the radius of the helix.

Answer 1

As per the question,

Charge of the particle =q

Magnetic field =B

Velocity =v

Let the angle between the magnetic field and the velocity is $\theta$

So,

velocity along the tangential direction to the helix =v$\sin\theta$

now, centripetal force =magnetic force

$\dfrac{m(v\sin\theta)^2}{R}=qvB\sin\theta$

$\Rightarrow R=\dfrac{qB}{mv\sin\theta}$

here R is the radius of the helix.

The horizontal component of the velocity is responsible for the motion in the horizontal direction of the helix.