Find the frequency of revolution of an electron with an energy of 100 eV in a uniform magnetic

step 1 In this question, we have an electron. It has an energy of a hybrid EVE, moving in a region of m

Find the frequency of revolution of an electron with an...

Find the frequency of revolution of an electron with }\end{array}$ an energy of $100 \mathrm{eV}$ in a uniform magnetic field of magnitude $35.0 \mu \mathrm{T}$. (b) Calculate the radius of the path of this electron if its velocity is perpendicular to the magnetic field.

Key Concepts

Cyclotron Frequency

This concept pertains to the frequency at which a charged particle, such as an electron, orbits within a uniform magnetic field. The cyclotron frequency is determined solely by the charge-to-mass ratio of the particle and the magnetic field strength, and is independent of the particle’s speed. It is fundamental in understanding the behavior of charged particles in accelerators and magnetic confinement devices.

Lorentz Force in a Magnetic Field

When a charged particle moves through a magnetic field, it experiences a force known as the Lorentz force. This force acts perpendicular to both the velocity of the particle and the direction of the magnetic field, causing the particle to move in a circular path. Understanding this force is crucial for analyzing the motion of electrons in magnetic fields.

Centripetal Motion and Radius of Curvature

A particle moving in a circle requires a centripetal force to maintain its curved trajectory. For an electron in a magnetic field, the centripetal force needed for circular motion is provided by the Lorentz force. By equating these forces, one can derive the radius of the circular path, an important concept in both classical mechanics and electromagnetic theory.

Relationship Between Kinetic Energy and Velocity

The kinetic energy of a particle is related to its velocity by the equation K = (1/2)mv^2. This relationship allows for the determination of the electron’s speed when its kinetic energy is provided. Converting energy units (for example, from electron volts to joules) is a necessary step in using this relationship in practical calculations involving electron motion in magnetic fields.

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