An electric dipole of moment $\vec{P}$ is placed in a uniform electric field $\vec{E}$ . Then
$(i)$ the torque on the dipole is $\vec{P} \times \vec{E}$ .
$(i i)$ the potential energy of the system is $\vec{P} . \vec{E}$ .
$(i i i)$ the resultant force on the dipole is zero.
Choose the correct option.

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$(i), (i i)$ and $(i i i)$ are correct.

$(i)$ and $(i i i)$ are correct and $(i i)$ is wrong.

Only $(i)$ is correct.

$(i)$ and $(i i)$ are correct and $(i i i)$ is wrong.

answer is B.

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Detailed Solution

In a uniform electric field $\vec{E}$ , dipole experiences a torque $\vec{τ}$ given by $\vec{τ} = \vec{P} \times \vec{E}$ but experiences no force.

The potential energy of the dipole in a uniform electric field $\vec{E}$ is $U = - \vec{P} . \vec{E}$

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