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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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