Answer to Question #134975 in Classical Mechanics for Afraid

Question

A charged particle moves in a helical path under the influence of a constant
magnetic field. The initial velocity is such that the component along the
magnetic field is twice the component in the plane normal to the magnetic
field.
The ratio l / R of the pitch l to the radius R of the helical path is

Answer 1

Solution

According to given question data diagram can be shown as below

Now by using theory and data of question components of velocity

( parallel v and perpendicular v') can relate

By below relation

v=2v'...... eq. 1

Now

Pitch of this helix path is given by

$l=v.T$

$l=v \frac{2 \pi R}{v'}$

Now using equation 1

Therefore

$l=2v'\frac{2\pi R}{v'}=4\pi R$

Therefore ratio of $l$ and $R$ is given by

$\frac{l}{R}=4\pi$

Therefore ratio of pitch to radius of pitch is $4\pi.$