Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 37 of 127
The speed of electromagnetic waves \(c\) in free space in terms of permittivity \(\varepsilon_0\) and permeability \(\mu_0\) is given by:
A
\(c = \sqrt{\mu_0 \varepsilon_0}\)
B
\(c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\)
C
\(c = \frac{1}{\mu_0 \varepsilon_0}\)
D
\(c = \frac{\mu_0}{\varepsilon_0}\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \(c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\)
Concept:

Maxwell's equations predict that electromagnetic waves propagate through vacuum at a speed determined by the fundamental electromagnetic constants of free space.

Formula / Reaction:

$$c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3 \times 10^8\text{ m/s}$$

Solution:

  • Substituting \(\mu_0 = 4\pi \times 10^{-7}\text{ T}\cdot\text{m/A}\) and \(\varepsilon_0 = 8.854 \times 10^{-12}\text{ C}^2/(\text{N}\cdot\text{m}^2)\):


  • \(c = \frac{1}{\sqrt{(4\pi \times 10^{-7})(8.854 \times 10^{-12})}} \approx 3.00 \times 10^8\text{ m/s}\).


Why other options are incorrect:

  • Opt_A: Places the constant product in the numerator, which gives units of \(\text{s/m}\).


  • Opt_C: Omits the square root.


  • Opt_D: Uses an incorrect ratio of the constants.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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