A particle of mass m and charge Q moving with velocity ∇⃗ describes a circular path of radius R

step 1 As we all know that F is equal to QV cross B. Solving it further, here F is perpendicular to the

A particle of mass m and charge Q moving with velocity ∇⃗...

A particle of mass $m$ and charge $Q$ moving with velocity $\vec{\nabla}$ describes a circular path of radius $R$ when subjected to a uniform transverse magnetic field of inductance $B_{2}$ The work done by the field when the particle completes one full circle is : (a) $B Q v(2 \pi R)$ (b) $\left(\frac{m v^{2}}{R}\right) 2 \pi R$ (c) zero (d) $B Q(2 \pi R)$

A particle of mass $m$ and charge $Q$ moving with velocity $\vec{\nabla}$ describes a circular path of radius $R$ when subjected to a uniform transverse magnetic field of inductance $B_{2}$
The work done by the field when the particle completes one full circle is :
(a) $B Q v(2 \pi R)$
(b) $\left(\frac{m v^{2}}{R}\right) 2 \pi R$
(c) zero
(d) $B Q(2 \pi R)$

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Key Concepts

Circular Motion in a Magnetic Field

When a charged particle moves perpendicularly to a uniform magnetic field, the magnetic force acts as a centripetal force, causing the particle to move in a circular path. The balance between the magnetic force and the centripetal force determines the radius of the circle, but despite this continuous force, no work is done as the force and displacement remain perpendicular.

Lorentz Force

The Lorentz force, given by F = q(v × B), is the fundamental law describing the force experienced by a charged particle moving in a magnetic field. This force is always perpendicular to both the velocity of the particle and the magnetic field, which is crucial in understanding the motion of charged particles in magnetic environments.

Work Done by Magnetic Fields

Work is defined as the dot product of force and displacement. Since the magnetic force on a charged particle is always perpendicular to its velocity, the dot product—and hence the work done—is zero. This means that while the magnetic force can change the direction of the particle's motion, it does not change the kinetic energy of the particle.

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