Question

A charge moving in a magnetic field B with velocity v at any angle theta to the magnetic field , the path of charged particle is 1) circular ,2) helical with constant pitch ,3) helical with variable pitch , 4) move in a straight line..​

Answer 1

Given:

A charge moving in a magnetic field B with velocity v at any angle theta to the magnetic field.

To find:

Trajectory of charged particle.

Solution:

Let's assume that charged particle is moving with velocity v at an angle of $\theta$ with magnetic field.

From the diagram. we can see that:

• $v\cos(\theta)$ component of velocity will provide the translational component for the charge.

• $v\sin(\theta)$ will provide the centripetal component for circular rotation of charge.

So, the charge will move in a helical path with constant pitch.

Radius of trajectory:

$\boxed{ \rm{r = \dfrac{m \{v \sin( \theta) \}}{Bq} }}$

Pitch:

$\boxed{ \rm{x = v \cos( \theta) \times t}}$

Hope It Helps.