Un ion con una sola carga que se mueve en un campo magnético uniforme de 7,5 ×10^-2 T completa

step 1 So for this question, we can start with the formula t equals 2 pi m over qb. And the first thing

Un ion con una sola carga que se mueve en un campo magnético...

Key Concepts

Uniform Magnetic Field

A uniform magnetic field is a region in space where the magnetic field strength and direction remain constant. In problems involving charged particles, it ensures that the force experienced by the particle is consistently perpendicular to its velocity, leading to uniform circular motion.

Lorentz Force

The Lorentz force is the force acting on a charged particle moving within a magnetic field, given by the cross product of the particle's velocity and the magnetic field vector. This force is responsible for the circular or helical trajectories of charged particles, as it always acts perpendicular to their motion.

Cyclotron Motion

Cyclotron motion describes the circular movement of a charged particle in a uniform magnetic field due to the Lorentz force. In this context, the particle’s path is a circle because the constant magnitude and perpendicular direction of the force act as a centripetal force keeping the particle in a constant-radius orbit.

Charge-to-Mass Ratio

The charge-to-mass ratio (q/m) is a key parameter for identifying particles in a magnetic field, as it determines the radius and frequency of the circular path during cyclotron motion. By relating the period of revolution and the magnetic field to the cyclotron frequency, one can calculate this ratio, which is invaluable in identifying the type of ion involved.

Period of Revolution

The period of revolution is the time taken by a charged particle to complete one full cycle in its circular path under the influence of a uniform magnetic field. This period is directly linked to the cyclotron frequency, which is given by the ratio of the charge times the magnetic field to the mass, making it essential for analyzing the dynamics of cyclotron motion.

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