Question

An electric dipole consist of two opposite charges each of magnitude $1\mu C$ separated by a distance of $2cm.$ The dipole is placed in an external field of ${10}^5\text{N/C}$.The maximum torque on the dipole is:

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

Answer 1

The correct option is C $4\times {10}^{-3}J$

An electric dipole consist at two opposite charge each of magnitude $=1\mu C=1\times {10}^{-6}C$

distance $=2cm$

Exter field $={10}^{5}N/C$

maximum torque on the dipole $=?$

$q=1\times {10}^{-6}C,2a=2cm$

or, $=0.02cm$

$\therefore$ $P=q\times 2a$

$=(1\times {10}^{-6})\times 0.02$

$=2\times {10}^{-8}cm$

Intensity of the external electric field, $E=1.0\times {10}^{5}N/C$

(i) $Z_{max}=pE=(2\times {10}^{-8})(10\times {10}^5)=2\times {10}^{-3}N-m$

(ii) Net work done in turning the dipole from $0^0$ to ${180}^0$

i.e $W={\int }_{0^0}^{{180}^0}\overline{r}d\theta ={\int }_{0^0}^{{180}^0}pE\sin \theta d\theta$

$=pE{[-cos\theta ]}_{0^0}^{{180}^0}$

$=-pE({\cos 180}^0-\cos 0^0)$

$=2pE$

$=2\times (2\times {10}^{-8})(1\times {10}^5)J$

$=4\times {10}^{-3}J$