question_answer

An electric dipole consisting of two opposite chargcs 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 is :

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

B)  \[12\times {{10}^{-3}}Nm\]

C)  \[24\times {{10}^{-1}}Nm\]                       

D)  \[24\times {{10}^{-3}}Nm\]

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\[\theta =90{}^\circ ,\] \[\sin 90{}^\circ =1\] \[\therefore \]  \[\tau =qlE\]                 \[=2\times {{10}^{-6}}\times \frac{3}{100}\times 2\times {{10}^{5}}\]                 \[\tau =12\times {{10}^{-3}}Nm\]