Question

An electric dipole is held in a uniform electric field.
(i) Show that the net force acting on it is zero.
(ii) The dipole is aligned parallel to the field. Find the work in rotating it through the angle of ${180}^{\circ }$.

Answer 1

(I) Let an electric dipole is placed in a uniform electric field $\overrightarrow{E}$ , making an angle $\theta$ with the field ,

force on charge $+q$ ${\overrightarrow{F}}_{+q}=+q\overrightarrow{E}$ (along $\overrightarrow{E}$)

force on charge $-q$ ${\overrightarrow{F}}_{-q}=-q\overrightarrow{E}$ (opposite to $\overrightarrow{E}$)

as two equal and opposite forces are acting on the dipole therefore net force $\overrightarrow{F}=0$

(ii) We know that work done in rotating a electric dipole from ${\theta }_1$ to ${\theta }_2$ , ( where ${\theta }_1$ is the angle of dipole with electric field ) is given by ,

$W=pE(\cos {\theta }_1-\cos {\theta }_2)$

now given ${\theta }_1=0,{\theta }_2=180$

therefore $W=pE(\cos 0-\cos 180)=2pE$