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Q.
An electric dipole consists of two opposite charges, each of magnitude $1.0\, \mu C$ separated by a distance of $2.0 \, cm$. The dipole is placed in an external field of $10^5 \, NC^{-1}$. The maximum torque on the dipole is
$1 \times 10^{-6} C$ distance $=2 cm$ Exter field $=10^{5} N / C$ maximum torque on the dipole $=$ ?
$q =1 \times 10^{-6} C , 2 a =2 \,cm$
or, $0.02 \,cm $
$ \therefore P = q \times 2 a$
$ =\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) $Z_{\max }=p E=\left(2 \times 10^{-8}\right)\left(10 \times 10^{5}\right)=2 \times 10^{-3} N - m$
(ii) Net work done in turning the dipole from $0^{0}$ to $180^{\circ}$
i.e $W =\int\limits_{0^{\circ}}^{180^{\circ}} \overline{ r } d \theta=\int\limits_{0^{\circ}}^{180^{\circ}} pE \sin \theta d \theta$
$= pE [-\cos \theta]_{0^{0}}^{180^{\circ}} $
$=- pE \left(\cos 180^{\circ}-\cos 0^{0}\right) $
$=2 pE $
$=2 \times\left(2 \times 10^{-8}\right)\left(1 \times 10^{5}\right) J $
$=4 \times 10^{-3} J $