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Two equal and opposite charges \(4×10^{-8}C\) are placed \(2×10^{-2}\) cm away, from a dipole. If this dipole is placed in an external electric field of \(4×10^8NC^{-1}\), the value of maximum torque and the work done in rotating it through 180o will be

(A) \(64×10^{-4}Nm\) and \(64×10^{-4}J\)

(B) \(32×10^{-4}Nm\) and \(32×10^{-4}J\)

(C) \(64×10^{-4}Nm\) and \(32×10^{-4}J\)

(D) \(32×10^{-4}Nm\) and \(64×10^{-4}J\)

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The correct answer of this question is (D). 

Solution :

Maximum torque is given by

\(\iota_{max} = pE \)  (\(Sin \theta = 1\))

\(=(q2a)E\)  (\(p=q×2a\))

\(=(4×10^{-8}×2×10^{-4})×4×10^8\)

\(=32×10^{-4}Nm\)

If \(\theta = 180^o,\) then

\(= W=pE(1-cos 180^o)\)

\(=pE[1-(-1)]=2pE \)

\(=2×32×10^{-4}\)

\(=64×10^{-4}J\)

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