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CBSE Class 12-science Answered

Two  charge   conducting  spheres  of  radius  'R'   and   '2R'  firet  placed in  contact  and  then  seperated .  At  the  surface  of  the  sphere of  each  which  sphere  has  the   greater  value of  CHARGE , POTENTIAL , ENERGY  STORED ?
Asked by pardeepkumar2281 | 22 May, 2018, 09:13: PM
answered-by-expert Expert Answer
Let us assume, once two spheres are placed in contact both the surfaces of spheres getting uniform charge density.
 
Hence after separation the sphere whose radius is 2R having more surface area and more charge.
 
If total charge on sphere whose radius is R is q , then total charge on sphere whose radius is 2R is 4q, because the large sphere has 4 times of area of small sphere.
 
Potential V1 of sphere that has radius R is given by,   begin mathsize 12px style V subscript 1 space equals space fraction numerator q over denominator 4 pi epsilon subscript 0 R end fraction end style
Potential V2 of sphere that has radius 2R is given by,   begin mathsize 12px style V subscript 2 space equals space fraction numerator 4 q over denominator 4 pi epsilon subscript 0 open parentheses 2 R close parentheses end fraction space equals space fraction numerator 2 q over denominator 4 pi epsilon subscript 0 R end fraction end style
Stored Energy in sphere = begin mathsize 12px style 1 half C space V squared end style, where C is capacitance and V is potential. Capacitance of sphere of radius R is 4πε0R.
Since capacitance is directly proportional to radius and large sphere potential is twice that of large sphere, large sphere has stored energy 8 times compare to the stored energy in small sphere.
Answered by Thiyagarajan K | 19 Jun, 2018, 04:13: PM
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