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# Two equal and opposite charges $8 \times 10^{-8} C$ are placed $2 \times 10^{-2}$ cm away from a dipole . If this dipole is placed in an external electric field $2 \times 10^8 N/C$. the value of maximum torque and work done in rotating through $180^{\circ}$ will be :

$(A)\;64 \times 10^{-4} Nm \;and\; 64 \times 10^4 J \\ (B)\;32 \times 10^{-4} Nm \;and\; 32 \times 10^{-4} J \\ (C)\;64 \times 10^{-4} Nm \;and\; 32 \times 10^{-4} J \\ (D)\;32 \times 10^{-4} Nm \;and\; 64 \times 10^{-4} J$

$z= PE \sin \theta = q (2l) E \sin \theta$
$Z_{max}= q(2l)E$
$\qquad= 8 \times 10^{-8} (2 \times 10^{-2} \times 10^{-2} ) \times 2 \times 10^8$
$\qquad= 32 \times 10^{-4}Nm$
$w= PE(1- \cos \theta) =q(2l) \in (1- \cos \theta)$
$\qquad= 8 \times 10^{-8} (2 \times 10^{-2} \times 10^{-2} ) 2 \times 10 ^{8} \times (1-(-1))$
$\qquad= 64 \times 10^{-4}J$
Hence D is the correct answer.