`V_(A),V_(B),V_(C)`, ज्ञात कीजिए तथा यदि `V_(A)=V_(C)` हो तो आवश्यक शर्त क्या होगी।

Explanation

चालक गोले अथवा कोश के लिये
`V_("surface")V_("in")=(sigma)/(epsilon_(0))R`
`V_("out")=(sigma)/(epsilon_(0))(R^(2))/(r)" "` (जहाँ R = गोले अथवा कोश की त्रिज्या तथा r = केन्द्र से दूरी)
`V_(A)=(sigma a)/(in_(0))-(sigmab)/(in_(0))+(sigmac)/(in_(0))=(sigma)/(in_(0))(a-b+c)`
`V_(B)=(sigmaa^(2))/(in_(0)b)-(sigmab)/(in_(0))+(sigmac)/(in_(0))=(sigma)/(in_(0))((a^(2))/(b)-b+c),`
`V_(C)=(sigma a^(2))/(in_(0)c)-(sigmab^(2))/(in_(0)c)+(sigmac^(2))/(in_(0)c)=(sigma)/(in_(0))((a^(2)-b^(2)+c^(2))/(c))`
`rArr` अब यदि `V_(A)=V_(C)rArr(a-b+c)=(a^(2)-b^(2)+c^(2))/(c)rArrc (a-b)=a^(2)-b^(2)rArrc=a+b`