The Question is from neet-physics , and it was created by the author P.NARASIMHA

Question

A molecule of a substance has a permanent electric dipole moment of magnitude $10^{-29} \mathrm{~cm}.$ 2 mole of this substance is polarized (at low temperature) by applying a strong electrostatic field of magnitude $10^6 \mathrm{~Vm}^{-1}.$ What should be potential energy of its?  
[1 mole of the substance contains $6 	imes 10^{23}$ molecules]

P.NARASIMHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Potential energy of an electric dipole in an electric field
	**Related Topics**: Dipole moment, Electrostatics
	**Prerequisites**: Understanding of dipole moments and electrostatic potential energy calculations
## SOLUTION PATHWAY
**Given Information**:
		- Dipole moment, $p = 10^{-29} \mathrm{~cm} = 10^{-31} \mathrm{~m}$
		- Electric field, $E = 10^6 \mathrm{~Vm}^{-1}$
		- Number of moles, $n = 2$ moles (which equals to $2 	imes 6 	imes 10^{23}$ molecules)
**Method & Steps**:
1. Calculate the total number of molecules:
	Reasoning: Use Avogadro’s number to convert moles to molecules.
	Formula/Rule: $N = n 	imes N_A = 2 	imes 6 	imes 10^{23} = 1.2 	imes 10^{24}$ molecules
2. Calculate the potential energy of one dipole in the electric field:
	Working: The potential energy $U$ of a dipole in an electric field is given by $U = -pE$.
	Key Point: We need to use the absolute value of the dipole moment.
	Formula: $U_{single} = -pE = -10^{-31} \mathrm{~m} 	imes 10^6 \mathrm{~Vm}^{-1} = -10^{-25} \mathrm{~J}$
3. Calculate the total potential energy for all dipoles:
	Result: $U_{total} = N 	imes U_{single} = 1.2 	imes 10^{24} 	imes (-10^{-25} \mathrm{~J}) = -12 \mathrm{~J}$
	Verification: The calculations show the total energy is indeed -12 J.
## OPTION ANALYSIS
[A] :x: Incorrect calculation of total energy.
[B] ✓: Correct option, based on proper calculation of total energy.
[C] :x: Incorrect because it does not match the energy calculation.
[D] :x: Incorrect as it does not consider the total number of molecules.
## LEARNING AIDS
	**Common Mistakes**:
		1. Not using the correct units for dipole moment, ensure conversion is done correctly.
		2. Forgetting to account for all molecules when calculating total energy.
	**Quick Tips**:
		1. Always check the units when calculating potential energy.
		2. Remember the negative sign in the potential energy formula indicates stability.

P.NARASIMHA · Answer

$-6 \mathrm{~J}$

P.NARASIMHA · Answer

The correct Option is "$-12 \mathrm{~J}$"

P.NARASIMHA · Answer

$12 \mathrm{~J}$

P.NARASIMHA · Answer

$6 \mathrm{~J}$

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