A molecule of a substance has a permanent electric dipole moment of magnitude \(10^{-29} C m\). 2 mole of this substance is polarised (at low temperature) by applying a strong electrostatic fleld of magnitude \(10^6 Vm ^{-1}\). What should be potential energy of its ? (1 mole of substance contains \(6 \times 10^{23}\) molecules.)

A -6 J
B -12 J
C 12 J
D 6 J

Verified Solution

Answer & Solution

Correct Answer

(B) -12 J

Step-by-step Solution

Detailed explanation

(B)
Dipole moment of each molecules \(
=10^{-29} Cm
\)
As 1 mole of the substance contains \(6 \times 10^{23}\) molecules.
\(\therefore 2\) mole of the substance contains
\(2 \times 6 \times 10^{23}\) molecules.
Total dipole moment of all the molecules.
\(\begin{array}{l}
p=2 \times 6 \times 10^{23} \times 10^{-29} \\
p=12 \times 10^{-6} Cm
\end{array}\)
potential energy
\(
\begin{array}{l}
U=-pE \cos \theta \\
U=-12 \times 10^{-6} \times 10^6 \cos 0^{\circ} \\
U=-12 J
\end{array}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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