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CBSE Class 12-science Answered

please explain the attached que
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Asked by rohitraman1115 | 02 Jul, 2018, 08:46: PM
answered-by-expert Expert Answer
Electric field due to a uniformly charged solid sphere at a point d from center of sphere is given by
 
begin mathsize 12px style E left parenthesis d right parenthesis space equals space fraction numerator q over denominator 4 pi epsilon subscript 0 end fraction 1 over d squared space space w h e n space d space greater than space R E left parenthesis d right parenthesis space equals space fraction numerator q over denominator 4 pi epsilon subscript 0 end fraction d over R cubed space space w h e n space d space less than space R end style 
where q is the charge of sphere and R is its radius.
 
Electrical potential V at a point d, when d>R is given by
 
begin mathsize 12px style V left parenthesis d right parenthesis space equals space minus integral subscript negative infinity end subscript superscript d E left parenthesis r right parenthesis d r space equals space minus integral subscript negative infinity end subscript superscript d fraction numerator q over denominator 4 pi epsilon subscript 0 end fraction fraction numerator d r over denominator r squared end fraction space equals space fraction numerator q over denominator 4 pi epsilon subscript 0 end fraction 1 over d end style   ......................................(1)
 
Electric potential V at a point d, when d < R  is given by,
begin mathsize 12px style V left parenthesis d right parenthesis space equals space minus integral subscript negative infinity end subscript superscript d E left parenthesis r right parenthesis d r space equals space minus integral subscript negative infinity end subscript superscript R fraction numerator q over denominator 4 pi epsilon subscript 0 end fraction fraction numerator d r over denominator r squared end fraction space minus space integral subscript R superscript d fraction numerator q over denominator 4 pi epsilon subscript 0 R cubed end fraction r d r space equals space fraction numerator q over denominator 8 pi epsilon subscript 0 R end fraction open square brackets 3 minus d squared over R squared close square brackets end style  ..........................(2)
From the relation (1), it can be seen (1/d) variation for potential.
From relation (2), inside the sphere when d<R, qudratic variation with respect to distance d can be seen.
 
Hence graph-(3) represents the variation of potential
Answered by Thiyagarajan K | 03 Jul, 2018, 02:22: PM

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