A solid sphere of radius \(R\) has a charge \(Q\) distributed in its volume with a charge density \(\rho = kr\), where \(k\) and \(r\) are constants and \(r\) is the distance from its centre. If the electric field at \(r=\dfrac{R}{2}\) is \(\dfrac{1}{8}\) times that at \(r=R\), the value of \(a\) is:
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For spherical charge distributions:
\[
E(r) \propto r^{n} \Rightarrow \text{compare ratios using powers of } r
\]
Gauss law simplifies power-law charge densities.