第四届泛珠三角物理奥林匹克竞赛.pdf
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Pan Pearl 08 Solution 泛珠08 解答
Q1: (4 points)
In the process energy and momentum are conserved, so
碰撞前后动量和能量守恒,因此
m v m v 0 m v +m v (1 point)
A 0 B Bx B By A A
m v2 m v2 =+m v2 +m v2 +2E (1 point)
A 0 A A B Bx B By
Where, vA is in the y-direction, we can get 其中vA 是沿Y-方向的速度。由此得
m (m −m )v2 −2Em
vA A B A 0 B , (1 point)
mA (mB +mA )
m m
A A
vBx v0 ,vBy =− vA . (1 point)
m m
B B
Q2: (6 points)
From Gauss theorem, the area density of the free charge at the surfaces of the conductor
plates is σ D . (0.5 points) 根据高斯定理,导电板上自由电荷面密度与板间电位移的
f
关系为σ D 。
f
In the air gap E E D / ε , while in the dielectric E D / εε . (0.5 points)
1 3 0 2 0
在空气中E E D / ε ,在介质内E D / εε ,电压为
1 3 0 2 0
d d d dD 1 dσf 1
(2 ) (2 )
V E =+ E + E =+ =+ ,
1 2 3
3 3 3 3ε ε 3ε ε
0 0
由此得
V 3ε ε
σf 0 . (1 point)
d +
2ε 1
3V ε (ε−1)
The bound charge isσb mε0 (E1 =−E2 ) m 0 . (1 point)
d 2ε+1
3V ε (ε−1)
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