JEE Mains · Physics · STD 12 - 8. Electromagnetic waves
A plane electromagnetic wave having a frequency \(n = 23.9\, GHz\) propagates along the positive \(z-\) direction in free space. The peak value of the electric field is \(60\, V/m\). Which among the following is the acceptable magnetic field component in the electromagnetic wave?
- A \(\vec B = 2 \times {10^{ - 7}}\,\sin \,\left( {1.5 \times {{10}^2}x + 0.5 \times {{10}^{11}}t} \right)\hat j\)
- B \(\vec B = 60\,\sin \,\left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)\hat k\)
- C \(\vec B = 2 \times {10^{ - 7}}\,\sin \,\left( {0.5 \times {{10}^3}z - 1.5 \times {{10}^{11}}t} \right)\hat i\)
- D \(\vec B = 2 \times {10^{7}}\,\sin \,\left( {0.5 \times {{10}^3}z + 1.5 \times {{10}^{11}}t} \right)\hat i\)
Answer & Solution
Correct Answer
(C) \(\vec B = 2 \times {10^{ - 7}}\,\sin \,\left( {0.5 \times {{10}^3}z - 1.5 \times {{10}^{11}}t} \right)\hat i\)
Step-by-step Solution
Detailed explanation
Magnetic field when electromagnetic wave propagates in \(+z\) direction. \(\mathrm{B}=\mathrm{B}_{0} \sin (\mathrm{kz}-\omega \mathrm{t})\) where \(\mathrm{B}_{0}-\frac{60}{3 \times 10^{8}}=2 \times 10^{-7}\) \(\mathrm{k}=\frac{2 \pi}{\lambda}=0.5 \times 10^{3}\)…
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