A molecule of a substance has a permanent electric dipole moment of magnitude 10⁻²⁹ C m. Two moles of this substance are polarised (at low temperature) by applying a strong electrostatic field of magnitude 10⁶ V m⁻¹. What is the potential energy of the dipoles in this field? [1 mole of the substanc…

Question

A molecule of a substance has a permanent electric dipole moment of magnitude 10⁻²⁹ C m. Two moles of this substance are polarised (at low temperature) by applying a strong electrostatic field of magnitude 10⁶ V m⁻¹. What is the potential energy of the dipoles in this field? [1 mole of the substance contains 6×10²³ molecules]

Accepted Answer

(2) -12 J. Given: p=10⁻²⁹ C m per molecule; E=10⁶ V m⁻¹; 2 moles, so N=2×6×10²³=1.2×10²⁴ molecules. Idea: a strong field at low temperature polarises the sample completely - every dipole lines up with the field, θ=0°. One aligned dipole: U₁=-pE cos 0°=-10⁻²⁹×10⁶=-10⁻²³ J All of them: U=NU₁=1.2×10²⁴×(-10⁻²³)=-12 J The negative sign means energy would have to be supplied to pull the dipoles out of alignment.

Step-by-step solution

Why the other options are wrong