Question

请教两道物理电学题。200分。英文版的。求各位解答。。求详细。谢谢了.ans是答案





Answer 1

1. For a spherical capacitor, an integral of ∫(r1 to r2) dU = ∫(r1 to r2) Q/4πε0 1/r² dr
yields U=(Q/4πε0)(1/r1-1/r2).

Capacitance C=Q/U=3.3nC/220V=0.015 nF.
Since r2=4cm, r1=1/(1/r2+4πε0*U/Q)=1/(1/0.04+4*π*8.854e-12*220/3.3e-9)=3.09 cm.

2. (a) Q(r)=Qr³/R³ when r<R. Q(r)=Q when r>R.
E(r)=Q(r)/(4πε0r²)=Q/(4πε0)*r/R³ when r<R.
E(r)=Q(r)/(4πε0r²)=Q/(4πε0)/r² when r>R.

So take an integral of E(r), we get
V(r)=Q/(4πε0)/R+Q/(4πε0)*(R²-r²)/(2R³) when r<R.
V(r)=Q/(4πε0)/r when r>R.

(b) V(surface)-V(center)=V(R)-V(0)= -Q/(4πε0)/(2R).
When Q is positive, the center has higher potential.
When Q is negative, the surface has higher potential.

Answer 2

有文字版的么，或者把原文件发给我1241018272@qq.com