Physics Electrostatics SZABMU 2024
PMDC Verified Question 4 of 131
Q.181 The SI-unit of relative permittivity is/has
A
\( \frac{\text{C}^2}{\text{N m}^2} \)
B
\( \frac{\text{C}}{\text{N m}^2} \)
C
\( \frac{\text{C}^{-2}}{\text{N m}} \)
D
No unit
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: No unit
1. Concept:

Relative permittivity (often called the dielectric constant, \( \epsilon_r \)) is defined as the ratio of a material's absolute permittivity to the absolute permittivity of a perfect vacuum.

2. Formula:

$$ \epsilon_r = \frac{\epsilon_{medium}}{\epsilon_0} $$

3. Solution:

  • Because you are mathematically dividing a value by another value with the exact same SI units (\( \text{F/m} / \text{F/m} \)), the units perfectly cancel out.


  • This renders relative permittivity a pure, dimensionless scalar ratio.


4. Why other options are incorrect:

Option A is the correct unit for the absolute permittivity of free space (\( \epsilon_0 \)), not the relative ratio. Options B and C are incorrect mathematical variations.

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