In the xy - plane , the region y > 0 has a uniform magnetic field B 1 k ^ and the region y 0 has another uniform magnetic field B 2 k ^ . A positively charged particle is projected from the origin along the positive y − axis with speed v 0 = π m s − 1 at t = 0 , as shown in the figure. Neglect gravity in this problem. Let t = T be the time when the particle crosses the x − axis from below for the first time. If B 2 =

Step-by-step solution

Average speed along the ( x )-axis ( ( V _ x )= | V _ x | dt dt = d ₁+ d ₂ t ₁+ t ₂ (1) ) We also have, ( aligned & r ₁= mv qB ₁ , r ₂= mv qB B ₂ & since B ₁= B ₂ 4 aligned ) ( r ₁=4 r ₂ (2) ) Time in (B₁ B q B₁ =t₁ ) Time in ( B ₂ B qB ₂ = t ₂ ) Total distance along ( x )-axis ( d ₁+ d ₂=2 r ₁+2 r ₂=2 ( r ₁+ r ₂ )=2 (5 r ₂ ) ) Total time ( T = t ₁+ t ₂=5 t ₂ ) ( Average speed = 10 r ₂ 5 t ₂ =2 mv qB ₂ qB ₂ m =2 )