A charged particle moving in a uniform magnetic field when...

A charged particle moving in a uniform magnetic field when losses $4 \%$ of its kinetic energy, the radius of curvature of its circular path
(a) decreases by $2 \%$
(b) increases by $2 \%$
(c) increases by $4 \%$
(d) decreases by $4 \%$

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Key Concepts

Relationship between Kinetic Energy and Velocity

Since kinetic energy is defined as KE = (1/2)mv^2, any change in kinetic energy affects the particle's velocity. A reduction in kinetic energy results in a decrease in velocity, and because the radius of curvature is proportional to velocity, this leads to a corresponding reduction in the radius of the circular path.

Charged Particle Motion in a Magnetic Field

When a charged particle enters a uniform magnetic field, it experiences a Lorentz force that is always perpendicular to its velocity. This perpendicular force causes the particle to undergo circular or cyclotron motion, with characteristics determined by the particle's velocity, charge, mass, and the strength of the magnetic field.

Radius of Curvature

The radius of the circular path a charged particle follows in a magnetic field, often known as the cyclotron radius, is given by the equation r = mv/(qB). This shows that the radius depends directly on the particle's momentum (mass times velocity) and inversely on its charge and the magnetic field strength.

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