[Case Study, Q30 contd.] (iv)(a) A molecule of dipole moment $3.0 ...

Question

[Case Study, Q30 contd.] (iv)(a) A molecule of dipole moment $3.0\times10^{-30}$ C·m is placed in a uniform electric field of $2\times10^4\ NC^{-1}$. Find the maximum torque experienced by this molecule.

OR (b) An electric dipole made of two point charges +2pC and −2pC, separated by 1mm, is placed in a uniform field of $2\times10^5\ NC^{-1}$. Find the work done in rotating it from stable to unstable equilibrium.

Accepted Answer

Part (a): Step 1: Maximum torque $=pE\sin90°=pE$ (maximum when dipole is perpendicular to field).

Step 2: $\tau_{max} = 3.0\times10^{-30}\times2\times10^4 = 6.0\times10^{-26}$ N·m.

Step 3: Answer: (B) $6.0\times10^{-26}$ N·m.

Part (b) OR: Step 1: $p = q\times d = 2\times10^{-12}\times1\times10^{-3} = 2\times10^{-15}$ C·m.

Step 2: Work done rotating from stable ($\theta=0$) to unstable ($\theta=180°$) equilibrium: $W=pE(\cos0°-\cos180°) = pE(1-(-1))=2pE$.

Step 3: $W = 2\times2\times10^{-15}\times2\times10^5 = 8\times10^{-10}$ J.

Step 4: Answer: (C) $8\times10^{-10}$ J.

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