Understanding the Concepts
* Charged Particle in a Magnetic Field: When a charged particle moves through a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field direction. This force causes the particle to move in a circular path.
* Period of Circular Motion: The period of a circular motion is the time it takes for a particle to complete one full revolution.
The Formula
The period of a charged particle moving in a uniform magnetic field is given by:
```
T = (2πm) / (qB)
```
Where:
* T is the period
* m is the mass of the particle
* q is the magnitude of the charge of the particle
* B is the strength of the magnetic field
Analyzing the Change
In your scenario, we're only changing the mass of the particle (increasing it tenfold). Let's see how this affects the period:
* Direct Proportionality: Notice that the period (T) is directly proportional to the mass (m). This means that if you increase the mass, the period will also increase proportionally.
Conclusion
If a second particle with the same electric charge but ten times the mass enters the field at the same velocity, the period of its circular motion will be ten times greater than the original particle.
Important Note: This analysis assumes a uniform magnetic field. If the field is not uniform, the motion becomes more complex, and the period will not be easily calculated.
