An electric dipole of dipole moment $\vec{p} = (p_{1} \hat{i} + p_{2} \hat{j})$ is placed in a uniform electric field $\vec{E} = (c \hat{i} - d \hat{j})$ such that maximum possible torque is experienced by the dipole. Then $\frac{p_{1}}{p_{2}}$ is equal to

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$\frac{d}{c}$

$\frac{d + c}{d - c}$

$\frac{d - c}{d + c}$

$\frac{d^{2} + c^{2}}{cd}$

answer is A.

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Detailed Solution

Since the dipole experiences maximum torque, the angle between $\vec{P} and \vec{E}$ must be $90^{o}$

$∴ \vec{P} . \vec{E} = 0 \Rightarrow (p_{1} \hat{i} + p_{2} \hat{j}) . (c \hat{i} - d \hat{j}) = 0 \Rightarrow \frac{p_{1}}{p_{2}} = \frac{d}{c}$

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