Q.

There is spherical symmetric charge distribution around origin. The electrostatic potential (in Volts) at a distance ‘r’ from origin is given as V=Kr44 where K is a positive constant. The slope of tangent drawn to volume charge density vs ‘r’ graph at r=12m  is  αKε0. Then find value of 'α'.

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answer is 5.

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Detailed Solution

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From gauss law for spherical space charge density  
dEdr+2Er=ρ0 ρ=5K0r2 dρdr|r=12m=5K0
So, value of α is 5

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There is spherical symmetric charge distribution around origin. The electrostatic potential (in Volts) at a distance ‘r’ from origin is given as V=−Kr44 where K is a positive constant. The slope of tangent drawn to volume charge density vs ‘r’ graph at r=12m  is  αKε0. Then find value of 'α'.