Question

29. A charge q and mass m moving with velocity v enters a region of magnetic field B at an angle 0. Which ofthe following represents the correct graph for pitch w.r.t. angle theta?​

Answer 1

Explanation:

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Answer 2

Given,

Charge = q

Mass of the charge = m

Initial Velocity = v

Magnetic field = B

The charge enters the magnetic field region at an Angle of 0°.

To Find,

The graph for pitch w.r.t. angle theta.

Solution,

As the charge enters the magnetic field region at an angle of 0°, it represents that the uniform magnetic field is parallel to the motion of the charge.

We know, Force on a charge in a uniform magnetic field,

F = q (v x B)

where, v = velocity vector

B = magnetic field vector

In this case, $\theta$ = 0°

F = qvB sin$\theta$ = 0   [as sin0° = 0]

So, no force will be applied to the charge by the magnetic field.

Now, to find pitch, we need to find the distance moved by the particle along the direction of the magnetic field in one rotation.

Here, $v_p$ = velocity of the charge parallel to the magnetic field

$v_p$ = v cos$\theta$ = v (here)

T = time period

$P = v_p * T\\P = \frac{2\pi m v_p}{qB} \\P = \frac{2\pi m v}{qB}$

so, the pitch will be constant w.r.t angle $\theta$.

Therefore, the graph for pitch w.r.t $\theta$ will be a straight line parallel to the axis  $\theta$ represented.