An electric dipole $\vec{P} = p \hat{i}$ is placed at the origin. A point charge +Q is placed at point A (–a, b). Then the ratio $\frac{b}{a}$ for which the electric field at B(0,b) will be zero is

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${(\frac{p}{Qa})}^{\frac{1}{3}}$

${(\frac{Qa}{P})}^{\frac{1}{3}}$

${(\frac{ap}{Q})}^{\frac{1}{2}}$

${(\frac{p}{Q})}^{\frac{1}{3}}$

answer is B.

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Detailed Solution

$\frac{1}{4 {πε}_{o}} . \frac{p}{b^{3}} = \frac{1}{4 {πε}_{o}} \frac{Q}{a^{2}} \Rightarrow \frac{b^{3}}{a^{2}} = \frac{P}{Q} \Rightarrow \frac{b}{a} = {(\frac{p}{Qa})}^{\frac{1}{3}}$

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