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[ROGER2004070 (~築夢之路~)]

A conducting sphere of radius R and charge Q covered by a dieletric

spherical shell of dieletric constant k with outer radius 2R


問:How much energy is needed to build up this electrical field distribution?


這題只有答案 沒有算式 但我算的跟答案有些許不同

有沒有空閒的大大要幫我CHECK一下哪裡有問題?

我是用能量密度法來算的

1.r < R , E = 0
                         Q               2R
2.R < r < 2R , E = -------------- , Ue=∫   1/2(kε)E^2 * 4πr^2 dr
                    4π(kε) r^2         R
                                             Q^2
                                      = -------------
                                          16π(kε)R

                   Q             ∞
3.r > 2R , E = ---------- , Ue=∫   1/2(ε)E^2 * 4πr^2 dr
                4πεr^2         2R
                                     Q^2
                              = ------------
                                   16π(ε)R


然後2個再相加.....

                 Q^2
不過答案是給 ----------(1/2 + 1/K)
               16πεR

先謝了～


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