Question

Which one of the conditions can cause a particle to move with uniform circular motion in a uniform magnetic field?

A. the charged particle should be moving perpendicular to the magnetic force and parallel to the b field.
B. the charged particle should be moving parallel to the magnetic force and perpendicular to the b field.
C. the charged particle has to be positive and it should be moving in a direction opposite to a uniform b field.
D. the b field should be uniform and a charged particle should be moving perpendicular to the b field.
E. the charged particle has to be positive and should be moving parallel to the b field.

Answer 1

The condition that can cause a particle to move with uniform circular motion in a uniform magnetic field is when the charged particle is moving perpendicular to the magnetic force and parallel to the B field.

Step-by-step explanation:

In order for a particle to move with uniform circular motion in a uniform magnetic field, the charged particle should be moving perpendicular to the magnetic force and parallel to the B field. This means that option A is the correct condition.

Uniform circular motion of a charged particle in a uniform magnetic field is governed by the principles of electromagnetic forces. When a charged particle, such as an electron, enters a magnetic field perpendicular to its velocity, it experiences a Lorentz force that acts perpendicular to both the particle's velocity and the magnetic field. This force compels the particle to move in a circular path.

The condition for uniform circular motion in a magnetic field is when the magnetic force exactly balances the centripetal force required for circular motion. This occurs when the velocity of the charged particle is perpendicular to the magnetic field lines and the magnitude of the magnetic force equals the centripetal force, given by the equation

�

�

=

�

�

2

�

F

c

​

=

r

mv

2

​

, where

�

m is the mass of the particle,

�

v is its velocity, and

�

r is the radius of the circular path.

In summary, for a particle to undergo uniform circular motion in a uniform magnetic field, its velocity must be perpendicular to the magnetic field, ensuring a balance between the magnetic force and the centripetal force.