Question

An electric dipole consisting of two opposite charges of $2\times {10}^{-6}C$ each, separated by a distance of 3 cm is placed in an electric field of $2\times {10}^{5}N/C$. The maximum torque on the dipole will be

• A. $12\times {10}^{-1}Nm$
• B. $12\times {10}^{-3}Nm$
• C. $24\times {10}^{-1}Nm$
• D. $24\times {10}^{-3}Nm$

Answer 1

The correct option is B $12\times {10}^{-3}Nm$

Let $2d$ be the separation between the charges of a dipole.
So, we can write $2d=3cm$

We know that torque acting on the dipole due to electric field is given by
$\overrightarrow{\tau }=\overrightarrow{P}\times \overrightarrow{E}$
(Here $P$ is dipole moment and $E$ is electric field)
$⟹\tau =PEsin\theta$

For $\tau$ to be maximum, the angle between dipole moment and electric field must be ${90}^0$
$⟹{\tau }_{max}=PE$
$⟹{\tau }_{max}=(q\times 2d)(2\times {10}^{5}N/C$)
$⟹{\tau }_{max}=(2\times {10}^{-6}\times 3\times {10}^{-2}\times 2\times {10}^5)Nm$
$\therefore {\tau }_{max}=12\times {10}^{-3}Nm$