• A charged particle with charge q is moving with speed v in a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendiculuar to the same magnetic field. The time to complete one full circular revolution for the first particle T1. The time to complete one full circular revolution for the particle moving with speed 2v
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To determine the time to complete one full circular revolution for each particle, we can use the formula for the period of a charged particle moving in a magnetic field.
The period (T) is defined as the time it takes for one full circular revolution. It can be found using the formula:
T = 2πm/qB
Where:
- T is the period (time to complete one full circular revolution)
- m is the mass of the particle
- q is the charge of the particle
- B is the magnetic field strength
Given that the two particles have the same charge (q) and are moving in the same magnetic field (B), their periods will depend only on their masses (m) and velocities (v).
For the first particle moving with speed v:
T1 = 2πm/qB (1)
For the second particle moving with speed 2v:
T2 = 2πm/qB (2)
Comparing equations (1) and (2), we see that the periods (T) for both particles are the same. Therefore, the time to complete one full circular revolution for the particle moving with speed 2v will also be T1.