A positively charged sphere of radius $r_{0}$ , carries a volume charge density $δ$ . A spherical cavity of radius $\frac{r_{0}}{2}$ is then scooped out and left empty. $C_{1}$ is the centre of the sphere and $C_{2}$ is that of the cavity. What is the magnitude and direction of electric field at B.

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$\frac{17 {δr}_{0}}{54 \in_{0}} left$

$\frac{{δr}_{0}}{6 \in_{0}} left$

$\frac{17 δ_{0}}{54 \in_{0}} right$

$\frac{{δr}_{0}}{6 \in_{0}} right$

answer is A.

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Detailed Solution

$E = E_{whole sphere} - E_{cavity}$

$E = \frac{δr}{3 \in_{0}} - \frac{δ {(\frac{r}{2})}^{3}}{3 ε_{0} {(\frac{3 r}{2})}^{2}}$

$E = \frac{δr}{3 ε_{0}} (1 - \frac{1}{18})$

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