સમતલીય પોલરઇઝ્ડ વિદ્યુતચુંબકીય તરંગ શૂન્યાવકાશમાં એવી રીતે ગતિ કરે છે કે જેથી \(t\, = t_1\) સમયે \(z_1\) બિંદુ આગળ તેનું વિદ્યુતક્ષેત્ર શૂન્ય થાય છે. તેની નજીકમાં બીજો શૂન્ય \(z_2\) આગળ મળે છે. તો આ વિદ્યુતચુંબકીય તરંગની આવૃતિ કેટલી હશે?

A \(\frac{{3 \times {{10}^8}}}{{\left| {{z_2} - {z_1}} \right|}}\)
B \(\frac{{6 \times {{10}^8}}}{{\left| {{z_2} - {z_1}} \right|}}\)
C \(\frac{{1.5 \times {{10}^8}}}{{\left| {{z_2} - {z_1}} \right|}}\)
D \(\frac{1}{{{t_1} + \frac{{\left| {{z_{2 - }}{z_1}} \right|}}{{3 \times {{10}^8}}}}}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{{3 \times {{10}^8}}}{{\left| {{z_2} - {z_1}} \right|}}\)

Step-by-step Solution

Detailed explanation

Using \(E=E_{0}-e^{j(k z-\omega t)}\) Given, at \(t=t_{1}, z=z_{1}, E=0\) the next zero that occurs in it's neighborhood is at \(z_{2},\) the frequency of the electromagnetic wave at \(t_{2}\) \(e^{i\left(k z_{1}-\omega t_{1}\right)}=e^{i\left(k z_{2}-\omega x_{2}\right)}\)…

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

Explore more questions on app

From JEE Mains

Explore more questions on app