An electron and a positron are released from (0, 0, 0) and (0, 0, 1.5R) respectively, in a uniform magnetic field B = B0i, each with an equal momentum of magnitude p = eBR. Under what conditions on the direction of momentum will the orbits be non-intersecting circles?

This is a Long Answer Type Questions as classified in NCERT Exemplar Explanation- Since, B is along the x-axis, for a circular orbit the momenta of the two particles are in the y-z plane. Let P1 and P2 be the momentum of the electron and positron, respectively. Both traverse a circle of radius R of opposite sense. Let P1 make an angle? with the y-axis P2 must make the same angle. The centres of the respective circles must be perpendicular to the momenta and at a distance R. Let the centre of the electron be at Ce and of the positron at Cp . The coordinates of Ce is Ce= (0, -Rsin θ, Rcosθ ) Cp= (0, -Rsin θ, -32R-Rcosθ ) The circles of the two shall not overlap if the distance between the two centers are Greater than 2R. Let d be the distance between Cp and Ce. Let d be the distance between Cp and Ce. So d2= (2Rsin θ )2+ ( 32R-2Rcosθ )2 = 4R2sin2 θ + 94R 2-6R2cos θ +4R2cos2 θ = 4R2+ 94R 2-6R2cos θ Since d has to be greater than 2R So d2> 4R2 4R2+ 94R 2-6R2cos θ > 4R2 Cos θ <3/8

An electron and a positron are released from (0, 0, 0) and (0, 0, 1.5R) respectively, in a uniform magnetic field B = B₀i, each with an equal momentum of magnitude p = eBR. Under what conditions on the direction of momentum will the orbits be non-intersecting circles?

10 Views|Posted 9 months ago

Asked by Shiksha User

1 Answer

Sort by:

Answered by

Alok Kumar Singh | Contributor-Level 10

9 months ago

This is a Long Answer Type Questions as classified in NCERT Exemplar

Explanation- Since, B is along the x-axis, for a circular orbit the momenta of the two particles are in the y-z plane. Let P1 and P2 be the momentum of the electron and positron, respectively. Both traverse a circle of radius R of o