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A dipole of moment $\vec{p}$ is placed in uniform electric field $\vec{E}$ then torque acting on it is given by : -
A
$\vec{\tau} = \vec{p}\cdot\vec{E}$
B
$\vec{\tau} = \vec{p} \times \vec{E}$
C
$\vec{\tau} = \vec{p} + \vec{E}$
D
$\vec{\tau} = \vec{p} - \vec{E}$
Detailed Solution
The two charges of the dipole experience equal and opposite forces qE, which form a couple.
Torque magnitude $= qE \times 2a\sin\theta = pE\sin\theta$, directed perpendicular to both $\vec{p}$ and $\vec{E}$.
In vector form: $\vec{\tau} = \vec{p} \times \vec{E}$
(The dot product $-\vec{p}\cdot\vec{E}$ gives the potential energy, which is a scalar.)
Torque magnitude $= qE \times 2a\sin\theta = pE\sin\theta$, directed perpendicular to both $\vec{p}$ and $\vec{E}$.
In vector form: $\vec{\tau} = \vec{p} \times \vec{E}$
(The dot product $-\vec{p}\cdot\vec{E}$ gives the potential energy, which is a scalar.)