(2011? Hefei Sanmold) As shown in the figure, in the first quadrant of the xOy plane, there is a uniform magnetic field with a direction perpendicular to the paper surface and a magnetic induction int

(2011? Hefei Sanmold) As shown in the figure, in the first quadrant of the xOy plane, there is a uniform magnetic field with a direction perpendicular to the paper surface and a magnetic induction intensity of B.

Solution (1) When all particles move in the first quadrant, the particle that is 150° to the positive direction of the y-axis has the shortest movement time. The deflection angle of its speed is π6, and the shortest time is: tmin=π62πT =T12

When all particles move in the first quadrant, the particle that is 30° to the positive direction of the y-axis moves for the longest time, the deflection angle of its speed is 5π6, and the longest time is: tmax=5π62πT =5T12

So the time for all particles to pass through the x-axis △t=tmax-tmin=13T=2πm3qB

(2) The trajectory radius of the particle incident at an angle of 150° to the y-axis is ? R1＝asin30°＝2a

The leftmost coordinate is x1＝R1(1?cos30°)＝(2?3)a

The angle between it and the y-axis The particle trajectory radius is R2=asin30°=2a

The rightmost coordinate is x2=R2(1 cos30°)=(2 3)a

When the particle passes through the x-axis The position range of ＝mv1qB

∴