A deutron of kinetic energy 50 keV is describing a circular orbit of radius 0.5 m, is plane per

step 1 Hello students. In this question we have a deutron particle which is having the kinetic energy K

A deutron of kinetic energy 50 keV is describing a circular...

A deutron of kinetic energy $50 \mathrm{keV}$ is describing a circular orbit of radius $0.5 \mathrm{~m}$, is plane perpendicular to magnetic field $B$. The kinetic energy of proton that describes a circular orbit of radius $0.5 \mathrm{~m}$ in the same plane with the same magnetic field $B$, is (a) $200 \mathrm{keV}$ (b) $50 \mathrm{keV}$ (c) $100 \mathrm{keV}$ (d) $25 \mathrm{keV}$

A deutron of kinetic energy $50 \mathrm{keV}$ is describing a circular orbit of radius $0.5 \mathrm{~m}$, is plane perpendicular to magnetic field $B$. The kinetic energy of proton that describes a circular orbit of radius $0.5 \mathrm{~m}$ in the same plane with the same magnetic field $B$, is
(a) $200 \mathrm{keV}$
(b) $50 \mathrm{keV}$
(c) $100 \mathrm{keV}$
(d) $25 \mathrm{keV}$

Key Concepts

Kinetic Energy Relation in Magnetic Circular Motion

For a particle moving in a circular orbit in a magnetic field, the kinetic energy, given by K = (1/2)mv², can be linked to the radius and the magnetic field. By substituting the expression for velocity from the Larmor radius formula, kinetic energy becomes inversely proportional to the mass for fixed charge, magnetic field, and radius.

Mass and Charge Dependency

This concept emphasizes that, in a uniform magnetic field, particles with different masses but the same charge will follow circular orbits of the same radius only if their speeds (and hence kinetic energies) adjust appropriately. Specifically, for a constant orbital radius and magnetic field, a lighter particle must have a lower kinetic energy compared to a heavier one to satisfy the r = (mv)/(qB) relationship.

Charged Particle Motion in a Magnetic Field

This concept describes how charged particles experience a magnetic Lorentz force when moving in a magnetic field, causing them to follow curved paths, often circular, when their velocity vector is perpendicular to the field. The force is given by F = qvB, which is central to understanding motion in devices like cyclotrons.

Larmor (Cyclotron) Radius

The Larmor radius is the radius of the circular path that a charged particle follows under the influence of a magnetic field. It is calculated using r = (mv)/(qB) and shows that the radius depends directly on the particle’s mass and speed and inversely on its charge and the magnetic field strength.

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