Radius Of Charged Particle Path In Magnetic Field Gyroradius

Radius Of Charged Particle Path In Magnetic Field Gyroradius — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.

Radius of Charged Particle Path in Magnetic Field (Gyroradius) Applies to a charged particle moving in a uniform magnetic field. If the particle enters at an angle θ != 90°, 'v' is v perp = v sin(θ), and the path is helical. The magnetic Lorentz force is F = q(v x B). Magnitude is F = qvBsin(θ). For circular motion (θ=90°), F B = qvB. This magnetic force provides the necessary centripetal force: F c = mv²/r. Equating forces: qvB = mv²/r. Solving for r: r = mv / (qB). Magnetic field must be uniform in the region of motion. Gravitational and electric forces are neglected or zero. Applicable for non-relativistic speeds (v << c). For relativistic speeds, 'm' represents relativistic mass. Assuming 'v' is always total speed even when entering at an angle (must use perpendicular component). Thinking the magnetic field does work on the particle (it does zero work). Confusing the relationship r ∝ v with r ∝ √K (Kinetic Energy). Note that r = √(2mK)/qB.