A solid sphere of radius \( r \) has a charge \( Q \) distributed in its volume with a charge de...

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A solid sphere of radius \( r \) has a charge \( Q \) distributed in its volume with a charge density \( \rho=k r^{a} \) where \( k \) and \( a \) are constants and \( r \) is the distance from its centre. If the electric field at \( r=R / 2 \) is \( 1 / 8 \) times that at \( r=R \), find the value of \( a \).
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