Question

An electric dipole consists of two opposite charges, each of magnitude $1.0\mu C$ separated by a distance of $2.0cm$. The dipole is placed in an external field of $10^{5}N{C}^{-1}$. The maximum torque on the dipole is

• A. $0.2\times 10^{-3}Nm$
• B. $1\times 10^{-3}Nm$
• C. $2\times 10^{-3}Nm$
• D. $4\times 10^{-3}Nm$

Answer 1

Answer: (D)

$1\times 10^{-6}C$ distance $=2cm$ Exter field $=10^{5}N/C$ maximum torque on the dipole $=$ ?
$q=1\times 10^{-6}C,2a=2cm$
or, $0.02cm$
$\therefore P=q\times 2a$
$=\left(1\times 10^{-6}\right)\times 0.02$
$=2\times 10^{-8}cm$
Intensity of the external electric field, $E=1.0\times 10^{5}N/C$
(i) $Z_{\max }=pE=\left(2\times 10^{-8}\right)\left(10\times 10^5\right)=2\times 10^{-3}N-m$
(ii) Net work done in turning the dipole from $0^0$ to $180^{\circ }$
i.e $W=\underset{0^{\circ }}{\overset{180^{\circ }}{\int }}\overline{r}d\theta =\underset{0^{\circ }}{\overset{180^{\circ }}{\int }}pE\sin \theta d\theta$
$=pE[-\cos \theta {]}_{0^0}^{180^{\circ }}$
$=-pE\left(\cos 180^{\circ }-\cos 0^0\right)$
$=2pE$
$=2\times \left(2\times 10^{-8}\right)\left(1\times 10^5\right)J$
$=4\times 10^{-3}J$