Electric and magnetic fields E and B both point along +x. A particle of charge q and mass m is projected from the origin along +y with speed v. A target is at (x₀,0,0). For π²=10, E=1, x₀=1, m=2, q=10 (SI), find B in tesla so the particle hits the target when crossing the x-axis for the third time.
Physics · Magnetic effect of current
JEE Advanced

Question

Electric and magnetic fields E and B both point along +x. A particle of charge q and mass m is projected from the origin along +y with speed v. A target is at (x₀,0,0). For π²=10, E=1, x₀=1, m=2, q=10 (SI), find B in tesla so the particle hits the target when crossing the x-axis for the third time.

Physics · Magnetic effect of current

G1 Physics · Accepted Answer

Solve the Lorentz equations with E and B parallel to x. The transverse y-z motion is cyclotron motion with angular frequency ω=qB/m, while x has constant acceleration qE/m. Imposing y=0 at the third crossing and x=1 with π²=10 gives B=6 T.