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# A particle is projected in a plane perpendicular to a uniform magnetic field the area bounded by the path described by the particle is proportional to

Arun
25763 Points
2 years ago
1) We have,
Uniform Magnetic Field = B
Mass of Charge q = m
Let velocity be 'v' (.Constant. )
Since, Magnetic field is perpendicular to Velocity.
Fmag = qvB

2)Since, Magnetic force will always act perpendicular to velocity.
=> Radial Force in motion = Magnetic Force
r = mv/qB

Since, Radius of curvature is constant.
=> Trajectory of Charge 'q'is circle.
3) Using above R, where m, q, B are given .
Area of Circle, A : pi r²
A is proportional to v²
Hence, Area of Circle is proportional to Kinetic Energy.

Khimraj
3007 Points
2 years ago
AαR2 and R = m V/qB
RαV⇒AαV2
Ans : Kinetic Energy
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