Question

When a charged particle moves perpendicular to the magnetic field, its angular velocity of the circular motion does not depend on the:
1. Speed
2. Mass
3. Charge
4. Magnetic field intensity

Answer 1

Correct Answer - Option 1 : Speed

CONCEPT: 

Lorentz force:

• It is defined as the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B.
• The entire electromagnetic force on the charged particle is called the Lorentz force and is given by,

​⇒ FL = qE + qvBsinθ 

• A charged particle experiences a force when it moves in a magnetic field.

​⇒ F = qvBsinθ  

Where, F =  force due to magnetic field, q = magnitude of charge, v = speed of charge, B = magnetic field and θ = angle between v and B

CALCULATION:

• When the velocity of a charged particle is perpendicular to a magnetic field, it describes a circle and the angular velocity of the charged particle is given by:

​\(⇒ \omega=\frac{qB}{m} \)     -----(1)

• From the above equation, it is clear that the angular velocity depends on mass, charge, and magnetic field but it is independent of speed.
• Hence, option 1 is correct.