question_answer

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

A)   \[12\times {{10}^{-1}}\text{ }Nm\]

B)  \[12\times {{10}^{-3}}\text{ }Nm\]

C)  \[24\times {{10}^{-1}}Nm\]

D)  \[24\times {{10}^{-3}}\text{ }Nm\]

Correct Answer: B

Solution :

Torque \[(\tau )\] on a dipole in an electric field (E) is given by \[\tau =pE\,\sin \theta \] where p is electric dipole moment. \[\therefore \] \[\tau =(q\times l)E\,\sin \theta \] Torque is maximum, when \[\theta ={{90}^{o}},\] \[\sin \,\,{{90}^{o}}=I\] \[\therefore \] \[\tau =qlE\] \[=2\times {{10}^{-6}}\times \frac{3}{100}\times 2\times {{10}^{5}}\] \[\tau =12\times {{10}^{-3}}Nm\]