Two opposite and equal charges 4 × 10-8 coulomb when placed 2 × 10-2 cm away, from a dipole. If this dipole is placed in an external electric field 4 × 108 newton/coulomb, the value of maximum torque and the work done in rotating it through 180° will be

Given q = 4 × 10-8 C , 2a = 2 × 10-2 cm(i) τmax=pEcos⁡0∘θ=0∘,τmax=pE,τmax=(q×2a)E(ii) Work done in rotating it through 180°W=PE⁡cos⁡θ1−cos⁡θ2=(q×2a)Ecos⁡0∘−cos⁡180∘=(q×2a)E(1+1)W=2(q×2a)E

Two opposite and equal charges 4 × 10-8 coulomb when placed 2 × 10-2 cm away, from a dipole. If this dipole is placed in an external electric field 4 × 108 newton/coulomb, the value of maximum torque and the work done in rotating it through 180° will be

Given q = 4 × 10-8 C , 2a = 2 × 10-2 cm(i) τmax=pEcos⁡0∘θ=0∘,τmax=pE,τmax=(q×2a)E(ii) Work done in rotating it through 180°W=PE⁡cos⁡θ1−cos⁡θ2=(q×2a)Ecos⁡0∘−cos⁡180∘=(q×2a)E(1+1)W=2(q×2a)E

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Two opposite and equal charges 4 × 10^-8 coulomb when placed 2 × 10^-2 cm away, from a dipole. If this dipole is placed in an external electric field 4 × 10⁸ newton/coulomb, the value of maximum torque and the work done in rotating it through 180° will be

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64 × 10^-4 Nm and 64 × 10^-4 J

32 × 10^-4 Nm and 64 × 10^-4 J

64 × 10^-4 Nm and 32 × 10^-4 J

32 × 10^-4 Nm and 32 × 10^-4 J

answer is B.

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Detailed Solution

Given q = 4 × 10^-8 C , 2a = 2 × 10^-2 cm
(i) $τ_{max} = pEcos 0^{\circ} (θ = 0^{\circ}), τ_{max} = pE, τ_{max} = (q \times 2 a) E$
(ii) Work done in rotating it through 180°
$\begin{array}{l} W = PE (\cos θ_{1} - \cos θ_{2}) = (q \times 2 a) E (\cos 0^{\circ} - \cos 180^{\circ}) = (q \times 2 a) E (1 + 1) \\ W = 2 (q \times 2 a) E \end{array}$