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  • A particle of charge +q and mass m, after being accelerated from rest by a voltage V enters a region of a uniform magnetic field in which it describes a circular motion of radius r. How m

A particle of charge +q and mass m, after being accelerated from rest by a voltage V enters a region of a uniform magnetic field in which it describes a circular motion of radius r. How much time does the particle spend in the region of the field?

Option: 1

\mathrm{2 \pi \sqrt{\frac{m r}{2 q V}}}


Option: 2

\mathrm{\frac{1}{\pi r} \sqrt{\frac{2 q V}{m}}}


Option: 3

\mathrm{\pi r \sqrt{\frac{m}{2 q V}}}


Option: 4

\mathrm{2 \pi r \sqrt{\frac{m}{2 q V}}}


Answers (1)

best_answer

Since the particle describes a circular path, it is obvious that it enters the region of B with velocity v perpendicular to B as shown in Fig.

Since the kinetic energy of the particle remains constant (because its velocity vector is always perpendicular to the force vector which is radial), it describes a semi-circle in the region of the magnetic field. Since its K.E. (and hence its speed v ) remains constant, the time the particle takes to describe the semi-circle is.

              \mathrm{ t=\frac{\pi r}{v} }                 .....(1)
Also, kinetic energy = qV
or \mathrm{ \frac{1}{2} m v^2=q V }
  \mathrm{ \Rightarrow \quad v=\sqrt{\frac{2 q V}{m}} }       .....(2)
Using (2) in (1) we get
\mathrm{ t= {\pi} r \sqrt{\frac{m}{2 q V}} }

which is choice (3)

Posted by

Pankaj Sanodiya

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