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(a) An electric dipole of dipole moment $\overrightarrow{p}$ is placed in a uniform electric field $\overrightarrow{E}$ at an angle $\theta$ with it. Derive the expression for torque ( $\overrightarrow{\tau }$ ) acting on it. Find the orientation of the dipole relative to the electric field for which torque on it is (i) maximum, and (ii) half of maximum.

(b) Two point charges $q_{1}+1 \mu C$ and $q_{2}+4 \mu C$ are placed 2 m apart in air. At what distance from q1 along the line joining the two charges, will the net electric field be zero ?

Answers (1)

a) Let us consider, the force on either charge be ;-

$F=qE$

we know, the magnitude of torque is given as ;

$\tau =$ either force $\times$ perpendicular distance between them

therefore,

$\tau =qE\; 2a\; \sin \theta$

Such that, $p=2qa$ (From the definition of dipole moment)

$\tau =PE\sin \theta$

$\tau =p\times E$

i) i) for maximum Torque, dipole should be placed perpendicular to the direction of the electric field

ii) For half of the torque

$\theta=30^0$

b)

Let x be the distance from $q_1$ where electric field =0

Then the distance from $q_2$ is 2-x

$\\E_1\ and \ E_2 \ are \ opposite \ in\ direction\\E_1-E_2=0\\E_1=E_2\\\frac{k\times1\mu C}{x^2}=\frac{k\times2\mu C}{(2-x)^2}\\\\2-x=2x\\x=\frac{2}{3}m$

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Safeer PP

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