(1) 一尚未帶電的金屬小球,和一大小相等而帶電的同樣小球相接觸後,放置相
距r=6公分處,測得其互斥力為F=4達因,求
(a)帶電小球原有電量。
Ans: 1dyne=10^(-5)Newton, 1cm=0.01m
=> r=0.06(m), F=4/10^5(N)
F=kq*q/r^2 => q^2=F*r^2/k
q=r√(F/k)
=0.06√[4/(10^5*9*10^9)]
=0.06*2/(3*10^7)
=4*10^(-9)Coml.........ans
(b)如欲將兩球作用力減為F=1達因=10^(-5)N時,求兩球間應有之距離。
r^2=k*q^2/F
r=q*√(k/F)
=4*10^(-9)*√(9*10^9*10^5)
=36*10^(-2)
=0.36(m)
=36(cm)
(2) 兩電荷相距r=1m,其中一電荷為q1=10^(-9)C,另一電荷為q2=10^(-8)C,問
其間作用力為若干?
Ans:
F=k*q1*q2/r^2
=[9*10^9]*[10^(-9)]*[10^(-8)]/1^2
=9*10^(-8)Newton..........ans
(3) 設一靜指的電荷q1=-5*10^(-8)C。一正電荷q2=2*10^(-8)C,受電荷q之吸引
,自距q為r1=3m處被吸至距q為r2=2m。求此正電荷所增加的動能。
Ans:
F1=k*q1*q2/r1^2
F2=k*q1*q2/r2^2
U=(F2-F1)*(r1-r2)
=k*q1*q2(r1-r2)/(1/r2^2-1/r1^2)
=k*q1*q2*(r1*r2)^2/(r1+r2)
=9*10^9*(5*10^-8)*(2*10^-8)*(2*3)^2/(2+3)
=90*36/5*10^7
=648*10(-7)Joule.........ans
(4) 設一電荷量為q=2x10^-6C,求距離此點電荷1m及2m兩處間的電位差。
Ans:
V1=k*q/r1
V2=k*q/r2
delta(V)=V1-V2
=k*q(1/r1-1/r2)
=k*q*(r2-r1)/(r1*r2)
=9*10^9*(2*10^-6)*(2-1)/(1*2)
=18000/2
=9000(Volts)...........ans
(5) 二平行板面各為A=100cm^2,且兩板具大小相等而符號相反的電荷q=9x10^-
7C,則板間的介電材料中的電場強度為E=1.2x10^6N/C,試求材料的介電常數。
Ans: A=100/10000=0.01(m^2)
phi=E*A=k*q
k=E*A/q
=(1.2*10^6)*0.01/9*10^(-7)
=(12/9)*10^10
=(4/3)*10^10(N.m^2/C^2)........ans
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