Answer to Question #134975 in Classical Mechanics for Afraid

Question #134975
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
1
Expert's answer
2020-09-24T11:06:11-0400

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.Tl=v.T

l=v2πRvl=v \frac{2 \pi R}{v'}

Now using equation 1

Therefore

l=2v2πRv=4πRl=2v'\frac{2\pi R}{v'}=4\pi R

Therefore ratio of ll and RR is given by

lR=4π\frac{l}{R}=4\pi


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



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