[電磁] 算不同介電常數電容的問題

[yihsianghuan (unknown)]

A parallel-plate capacitor with a plate separation d has a capacitance
C1. A slab of dielectric material of dielectric constant K and thickness d is
inserted between the plates.

(A)Calculate the new capacitance C2 with the dielectric slab.

(B)If thickness of the inserted dielectric slab is d/2,calculate the new
capacitance C3 with the dielectric slab.


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推 waanapple:(A) C2=KC1 方法:先假設帶電Q由電場高斯定律求出E
→ waanapple:    註:還要假設電界質產生感應電荷q~然後....
→ waanapple:    最後得到:C2=[Q/(Q-q)]C1~~其中[Q/(Q-q)]=K
→ waanapple:(B) 看成兩電容串連(一含電界質K另一個不含~板距都d/2)
→ waanapple:    1/C3=1/2KC1+1/2C1 得C3
→ waanapple:註解:平行板電容推導:先設Q~由高斯得E~積分得V帶入C=Q/V