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Physics Question on Electric Charges and Coulomb's Law

A dipole of moment p→\overrightarrow{p} is placed in uniform electric field E→\overrightarrow{E} then torque acting on it is given by : -

A

τ→\overrightarrow{\tau} = p→.E→\overrightarrow{p}.\overrightarrow{E}

B

τ→\overrightarrow{\tau} = p→×E→\overrightarrow{p}\times \overrightarrow{E}

C

τ→\overrightarrow{\tau} = p→+E→\overrightarrow{p}+\overrightarrow{E}

D

τ→\overrightarrow{\tau} = p→−E→\overrightarrow{p}-\overrightarrow{E}

Answer

τ→\overrightarrow{\tau} = p→×E→\overrightarrow{p}\times \overrightarrow{E}

Explanation

Solution

The correct option is (B): τ→\overrightarrow{\tau} = p→×E→\overrightarrow{p}\times \overrightarrow{E}.
The dipole moment (p) of a dipole in the presence of a uniform electric field (E) can be expressed as p = qa, where 'q' represents the charge, and 'a' is the length of the dipole. When a dipole with a dipole moment 'p' is situated within a uniform electric field 'E,' it experiences a torque (τ). This torque (τ) can be calculated as either the force (F) applied to the dipole multiplied by the perpendicular distance (d) between the point of application of the force and the axis of the dipole or simply as τ = pEsinθ, where 'θ' represents the angle between the dipole moment and the electric field direction, and 'p' is the dipole moment. (or τ=p×E).