\(1.61\) સાપેક્ષ પરમીએબિલિટી (પારગમ્યતા) અને \(6.44\) જેટલી સાપેક્ષ પરાવૈદ્યુતાંક (પરમીટીવીટી) ધરાવતા માધ્યમાંથી એક વિદ્યુતચુંબકીય તરંગ પસાર થાય છે. જો આપેલ બિંદુએ ચુંબકીયક્ષેત્રની તીવ્રતા \(4.5 \times 10^{-2} \;Am ^{-1}\) હોય તો તે બિંદુ આગળ વિધુતક્ષેત્રની તીવ્રતા કેટલી હશે? (Given : permeability of free space \(\mu_{0}=4 \pi \times 10^{-7}\;NA ^{-2}\), speed of light in vacuum \(c =3 \times 10^{8} \;ms ^{-1}\) )

A \(16.96 \;Vm ^{-1}\)
B \(2.25 \times 10^{-2}\; Vm ^{-1}\)
C \(8.48 \;Vm ^{-1}\)
D \(6.75 \times 10^{6}\; Vm ^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(8.48 \;Vm ^{-1}\)

Step-by-step Solution

Detailed explanation

\(\mu_{ I }=1.61 \quad \epsilon_{ I }=6.44\) \(B =4.5 \times 10^{-2}\) \(E =\) \(?\) \(C =\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}} V =\frac{1}{\sqrt{\mu \epsilon}}\) \(\frac{ C }{ V }=\sqrt{\mu_{ r } \epsilon_{ r }}=\sqrt{1.61 \times 6.44}\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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