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

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KollegeApply · Accepted Answer

the kinetic energy When a particle of mass m carrying charge q is projected with speed v in a plane perpendicular to a uniform magnetic field B, the field tends to deflect the particle in a circular path of radius r. \therefore m v^2/r = qvB \Rightarrow r = mv/qB \text{ Now }, \text{ Area, A } = $\pi$ r^2 \Rightarrow A = $\pi$ \left( mv/qB \right)^2 \Rightarrow A = k v^2 \text{Here }, k = $\pi$ \left( m/qB \right)^2 Kinetic energy of the particle, E = $\frac{1}{2}$m v^2 Therefore, the area bounded is proportional to the kinetic energy.

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