Problem 34.25 (RHK)
A neutral particle is at rest in a uniform magnetic field of magnitude B. At time it decays into two charged particles each of mass m. (a) If the charge of one of the particles is q, we have to identify the charge of the other particle.(b) The two particles move off in separate paths both of which lie in the plane perpendicular to . At a later time the particles collide. We have to express the time from decay until collision in terms of m, B, and q.
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As a neutral particle has decayed into two charged particles, as one of them has charge q the charge of the other has to be . This follows from the conservation of charge.
As a neutral particle at rest decays into two charged particles each of mass m, from the principle of conservation of momentum it follows that if one has velocity the velocity of the other has to be .
As the particles move in magnetic field at right angles to the force on the two charged particles will be perpendicular to both and . The two particles will move in circular orbits. If one moves in the clockwise direction, the other will move in the counter-clockwise direction. Let the radii of their circular orbits be R. from the symmetry of the problem we expect the two particles to collide with each other after each has travelled a distance .
As each particle is undergoing circular motion with speed v and the centripetal force is provided by the magnetic field B on moving charge q, we have
the decayed particles will collide after a lapse of time