\(+z\) દિશામાં ગતિ કરતાં વિદ્યુતચુંબકીય તરંગ માટે આવૃતિ \(1\times10^{14}\, hertz\) અને વિદ્યુતક્ષેત્રનું મૂલ્ય \(4\, V/m\) છે. જો \({\varepsilon_0}=\, 8.8\times10^{-12}\, C^2/Nm^2\) હોય તો આ વિદ્યુતક્ષેત્રની સરેરાશ ઉર્જા ઘનતા કેટલી હશે?

A \(35 .2\times10^{-10}\, J/m^3\)
B \(35 .2\times10^{-11}\, J/m^3\)
C \(35 .2\times10^{-12}\, J/m^3\)
D \(35 .2\times10^{-13}\, J/m^3\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(35 .2\times10^{-12}\, J/m^3\)

Step-by-step Solution

Detailed explanation

Given: Amplitude of electric field, \(E_{0}=4\,\mathrm{v} / \mathrm{m}\) Absolute per mitivity, \(\varepsilon_{0}=8.8 \times 10^{-12}\, \mathrm{c}^{2}\, / \mathrm{N}-\mathrm{m}^{2}\) Average energy density \(u_{E}=?\) Applying formula, Average energy density…

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.

Same subject

લીસ્ટ \(I\) સાથે લીસ્ટ \(II\) યોગ્ય રીતે જોડો.

લીસ્ટ \(I\) (ભૌતિક રાશી)	લીસ્ટ \(II\) (પારિમાણિક સૂત્ર)
\((A)\) દબાણ પ્રચલન	\((I)\) \(\left[ M ^0 L ^2 T ^{-2}\right]\)
\((B)\) ઊર્જા-ઘનતા	\((II)\) \(\left[ M ^1 L ^{-1} T ^{-2}\right]\)
\((C)\) વિદ્યુતક્ષેત્ર	\((III)\) \(\left[ M ^1 L ^{-2} T ^{-2}\right]\)
\((D)\) ગુપ્ત ઉષ્મા	\((IV)\) \(\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]\)

JEE Mains 2023 Medium

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