IIT JEE , AIEEE Forum - Physics , Electricity - a solid sphere having charge q . mass density dir.prop. to radius. find the V AT CENTER

edison

Please verify as it should be charge density.

karthik2007

I think you mean that the charge density is proportional to the radius. So assuming the above, we have

$\rho$ = kR.

Assuming its the space charge distribution, the charge dq in a spherical shell of thickness dr is $dq = 4\pi kR^3 dR$

Hence Q = $\int^R_0 4\pi kR^3\, dR$ .

Q = $\pi kR^4$

Hence, using, $V_{center} = \frac{Q}{4\pi \epsilon_o R}$ , you can get your answer

akshay.khare91

if that is charge density then ans
is
KQ/r.