Question

Find the work required to rotate the system of charges $(+q,-q)$ connected by rod of mass $m$ and length $l$ by an angle of ${180}^{\circ }$.

• A. $\frac{4}{5}qlE$
• B. $\frac{7}{5}qlE$
• C. $\frac{6}{5}qlE$
• D. $\frac{3}{10}qlE$

Answer 1

The correct option is C $\frac{6}{5}qlE$

Work done by external force,

$W_{net}=U_f-U_i=-pE(\cos {\theta }_2-\cos {\theta }_1)$

$\Rightarrow W_{net}=-pE\left(\cos \right({180}^{\circ }+{53}^{\circ })-\cos {53}^{\circ })$

$\Rightarrow W_{net}=2pE\cos {53}^{\circ }=2\left(ql\right)E\times \frac{3}{5}$

$\therefore W_{net}=\frac{6}{5}qlE$

Hence, option $\left(c\right)$ is correct.

Tip : The dipole will experience a net clockwise restoring torque in the position $(\theta ={53}^{\circ })$ shown in figure. Thus, work is required to be done by external force to rotate by ${180}^{\circ }$.