(20 1 1 Xiamen simulation) (18 minutes) As shown in the figure, electrons with mass m and charge e are injected into the first quadrant from the coordinate origin O along the xOy plane.

(1) Let the radius of a particle moving in a magnetic field be r, which is obtained by Newton's second law: (2 points).

Electron range through y axis (2 points)

(2) As shown in the figure, the electrons with initial velocity along the positive direction of the X axis move to point P along the arc OA on the phosphor screen MN, (1 point).

The electrons whose initial velocity is in the positive direction of the Y axis move along the arc OC to the Q point on the phosphor screen MN (1 min).

Get from geometry knowledge (2 points)

(3) The electron injected in the direction of θ angle with the positive direction of X axis is taken as the research object, and the point where it emits magnetic field is E(x, y). Because it can hit the phosphor screen MN vertically after launch, there are:

x=-Rsinθ？ (2 points)

Y=R+Rcosθ (2 points)

That is, x 2 +(y-R) 2 =R 2 (2 points)

Also, when electrons are injected along the positive direction of the X axis, the boundary point of emission is point A; When incident along the positive direction of Y-axis, the exit boundary point is point C, so the boundary of the magnetic field with the smallest area is a part of a circle with (0, r) as the center and R as the radius, which is an area surrounded by solid arc in the figure, so the minimum area of the magnetic field range is: (4 points).