A particle of mass m and charge q is accelerated by a potentiol difference V volt and made to enter a magnetic field region at an angle `y` with the field. At the same moment another particle of same mass and charge is projected in the direction of the field from the same point. What should be the speed of the second particle so that the particles meet again and again after regular interval of time which should be minimum.Also find the time interval after which they meet and the distance travelled by the second particle during the interval

here, the first particle is projected into the magnetic field with an angle 'y' with the field. so its path will be helical. and the 2nd particle is projected along the field direction. the 2nd particle will meet the 1st one, after travelling a distance which is equal to the pitch of the helix traced by the 1st particle.

let v₁ be the speed of the 1st particle.

the kinetic energy gained by the 1st particle = qV.

from this we can find v₁ .

the 2nd particle must have a velocity which equal to that of 1st particle in the field direction. i.e.

v₂ = v₁ cos y.

the distance to be travelled = pitch

time taken = time period of revolution of the helix.