The frequency of circular motion for a charged particle moving around in the presence of a uniform magnetic field does not depend on ...
a)The radius of the circle
b)The mass of the particle
c)The charge of the particle
d)The magnitude of the magnetic field
e)Actually, it depends on all of the above quantities
I believe the answer is d because the magnetic field alone cannot alter the KE of a particle because it is perpendicular to the particle velocity
Is this correct?
No, your understanding is incorrect. The correct answer is b) The mass of the particle. The frequency of circular motion for a charged particle moving in a uniform magnetic field depends on the radius of the circle, the charge of the particle, and the magnitude of the magnetic field. The mass of the particle does not affect the frequency of circular motion.
Yes, your understanding is correct. The frequency of circular motion for a charged particle moving in a uniform magnetic field does not depend on the magnitude of the magnetic field (option d). The frequency of the motion, commonly known as the cyclotron frequency, is determined solely by the properties of the particle itself.
To explain further, a charged particle moving in a magnetic field experiences a force called the Lorentz force, given by the equation F = qvB, where q is the charge of the particle, v is its velocity, and B is the magnitude of the magnetic field. This force acts as a centripetal force that keeps the particle moving in a circular path.
The centripetal force required to keep the particle in circular motion is given by the equation F = mω²r, where m is the mass of the particle, ω is the angular velocity, and r is the radius of the circular path. Equating the Lorentz force and the centripetal force, we get qvB = mω²r.
Now, the frequency of the circular motion, ω, is defined as the rate at which the particle completes one full revolution or cycle. It can be expressed in terms of the kinetic energy of the particle and the magnetic field. Using the equation qvB = mω²r and the expression for the kinetic energy (KE) of the particle, KE = (1/2)mv², we can derive an expression for the cyclotron frequency, given by ω = qB/m.
From this equation, we can see that the frequency of circular motion (or cyclotron frequency) only depends on the charge of the particle (q) and its mass (m). It is independent of the radius of the circular path (r) and the magnitude of the magnetic field (B). Therefore, the correct answer is d) The magnitude of the magnetic field.