Final answer:
The question concerns the Physics concept of a charged particle moving in a circular path due to a perpendicular uniform magnetic field. The period of this motion is given by T = 2πm / (qB), depending on the particle's mass, charge, and magnetic field strength.
Explanation:
When a charged particle with mass m and charge q moves in a uniform magnetic field of magnitude B, which points perpendicular to the plane of the circle, it experiences a magnetic force that acts perpendicular to its velocity. This force causes the particle to move in a circular path. The period T of the circular motion is determined by the equation T = 2πm / (qB), where m is the mass of the particle, q is its charge, and B is the magnetic field strength.
The radius r of the circular path depends on the speed v of the particle perpendicular to the magnetic field. If the velocity of the particle is not perpendicular, then the component u of the velocity perpendicular to the field is used in calculations, resulting in a spiral motion instead of circular motion. The period T is consistent for uniform circular motion and is calculated by dividing the circumference of the path by the speed of the particle.
For a particle with given mass, charge, and magnetic field, the period can be worked out through the mentioned formula. For example, for a particle with mass 6.64 × 10⁻²27kg, charge 3.2 × 10⁻²19C, and magnetic field strength 0.050 T, the time it takes to complete one rotation around the circle is provided by substituting the values into the period equation.