CBSE-XI-Physics
35: Magnetic Field due to a Current
- #8A 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
(a) the velocity
(b) the momentum
(c) the kinetic energy
(d) none of these.digAnsr: cAns : (c) 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 \frac{m{v}^{2}}{r}=qvB``
`` \Rightarrow r=\frac{mv}{qB}``
`` \,\mathrm{\,Now\,},``
`` \,\mathrm{\,Area\,},A=\,\mathrm{\,\pi \,}{r}^{2}``
`` \Rightarrow A=\,\mathrm{\,\pi \,}{\left(\frac{mv}{qB}\right)}^{2}``
`` \Rightarrow A=k{v}^{2}``
`` \,\mathrm{\,Here\,},``
`` k=\,\mathrm{\,\pi \,}{\left(\frac{m}{qB}\right)}^{2}``
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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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