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CBSE Class 12-science Answered

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Asked by nagavalli72003 | 23 Apr, 2020, 02:28: AM
answered-by-expert Expert Answer
By generalized ohm's law, J = σ E  ...................(1)
 
where J is current density , σ is conductivity, E is electric field intensity.
 
Current through the spherical surface of radius r between the given concentrc metallic spheres is given by
 
I = Current density × Area = σ E × 4 π r2 ..................(2)
 
If conductivity σ of medium between concentric metallic spheres is given by, σ = kE  .........(3)
 
Then by substituting for conductivity in eqn.(2), we get current I = 4πr2 kE2 ..................(4)
 
We get electric field E from eqn.(4) as
 
begin mathsize 14px style E space equals space square root of fraction numerator I over denominator 4 pi k end fraction end root space 1 over r end style
Potential V between concentric metallic spheres of radii b and a ( b > a ) is given by
 
begin mathsize 14px style integral subscript a superscript b d V space equals space integral subscript a superscript b E space d r space equals space square root of fraction numerator I over denominator 4 πk end fraction end root integral subscript a superscript b space fraction numerator d r over denominator r end fraction space equals space square root of fraction numerator I over denominator 4 πk end fraction end root space ln b over a end style
Answered by Thiyagarajan K | 23 Apr, 2020, 05:39: PM
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