The Question is from neet-physics units-and-measurement conversion-of-units-for-one-system-to-another, and it was created by the author Mr. ANIL KUMAR.G

Question

The constant of proportionality $\frac{1}{{4{\rm{\pi }}{{\rm{\varepsilon }}_0}}}\;$ in Coulomb’s law has the following units

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: Coulomb's Law
	**Related Topics**: Units and Dimensions, Force, Charge, Permittivity
	**Prerequisites**: Understanding of Coulomb's Law and basic SI units.
## SOLUTION PATHWAY
**Given Information**:
	Coulomb's Law constant: $\frac{1}{4\pi\epsilon_0}$
	We need to find the units of this constant.
**Method & Steps**:
	1. Start with Coulomb's Law: $F = k \frac{q_1 q_2}{r^2}$, where $k = \frac{1}{4\pi\epsilon_0}$
		Reasoning: This is the fundamental equation we'll use to derive the units of the constant.
		Formula/Rule: Coulomb's Law
	2. Rearrange the equation to isolate k: $k = \frac{F r^2}{q_1 q_2}$
		Reasoning:  Isolate the constant to determine its units.
		Working: Algebraic manipulation.
	3. Substitute the SI units for each quantity:  $k = \frac{N m^2}{C * C} = \frac{N m^2}{C^2}$
		Reasoning: Replace force with Newtons (N), distance with meters (m), and charge with Coulombs (C).
		Key Point: Units of Force (N), Distance (m), and Charge (C).
	4. Express the result with negative exponents: $k = C^{-2} N m^2$
		Result: The final units of the constant.
		Verification: Units match the correct answer.
 ## OPTION ANALYSIS
[A] ✓: The correct units are derived as  $C^{-2} N m^2$.
[B] :x: Incorrect combination of units and exponents.
[C] :x: Incorrect combination of units and exponents.
[D] :x: Incorrect combination of units and exponents.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. **Incorrectly applying Coulomb's Law**:  Make sure to use the correct formula.
		2. **Mixing up SI units**: Ensure to use the correct units for force, charge, and distance.
	**Quick Tips**:
		1.  Remember the units of force, charge, and distance.
		2. Rearrange the formula to solve for the constant of proportionality.

Mr. ANIL KUMAR.G · Answer

The correct Option is "${{\rm{C}}^{ - 2}}{\rm{N}}{{\rm{m}}^2}$"

Mr. ANIL KUMAR.G · Answer

${{\rm{C}}^2}{{\rm{N}}^{ - 1}}{{\rm{m}}^{ - 2}}$

Mr. ANIL KUMAR.G · Answer

${{\rm{C}}^2}{\rm{N}}{{\rm{m}}^2}$

Mr. ANIL KUMAR.G · Answer

${{\rm{C}}^{ - 2}}{{\rm{N}}^{ - 1}}{{\rm{m}}^{ - 2}}$

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