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Zhaoqing Moore science mathematics
Solution: (1) charged particles do quasi-planar motion in electric field. Let the acceleration of charged particles in the electric field be a, which can be obtained from Newton's law of motion:

qE=ma? ①

Let the velocity of particles leaving the electric field into the magnetic field be v, the component velocity in the Y-axis direction be vy, and the movement time of particles in the electric field be t, then there are:

vy=at②

l=mv02qE=v0t③

v=v02+vy2④

According to the formula 1234, v=2v0⑤.

sinθ=v0v⑥

According to ⑤ ⑤ formula: sinθ=22⑦.

It can be obtained from formula ⑦: θ = 45 ⑧.

(2) After the particles enter the magnetic field, they move in a circle under the Lorentz force, as shown in the answer sheet.

The particle do uniform circular motion in a magnetic field, and that centripetal force provided by Lorentz force include:

qvB=mv2R

So there is a particle motion orbit radius: r = mvqb.

It can be seen from the answer diagram that if charged particles can pass through the magnetic field region without returning to the electric field, then the width d of the magnetic field should satisfy:

d≤R( 1+cosθ)? ⑩

The solution from participation: dmax = (1+2) mv0qb … (13)

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