Question:
The magnetic field in a plane electromagnetic wave is $B_y = 2 \times 10^{-7} \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t)$. The correct expression for electric field of the wave is:
The magnetic field in a plane electromagnetic wave is $B_y = 2 \times 10^{-7} \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t)$. The correct expression for electric field of the wave is:
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$E = cB$. Waves propagating in $+x$ have $(kx - \omega t)$, in $-x$ have $(kx + \omega t)$.
Updated On: Jun 6, 2026
- $E_z = 60 \sin(0.5 \times 10^3 x - 1.5 \times 10^{11} t)$
- $E_y = 2 \times 10^{-7} \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t)$
- $E_y = 2 \times 10^{-7} \cos(1.5 \times 10^3 x + 0.5 \times 10^{11} t)$
- $E_z = 60 \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t)$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Electromagnetic wave properties: $E_0 = c B_0$, wave travels in direction of $\vec{E} \times \vec{B}$.
Step 2: Meaning
$E_0 = 3 \times 10^8 \times 2 \times 10^{-7} = 60$ V/m.
Step 3: Analysis
Since $\vec{B}$ is along $y$ and wave propagates along $-x$, $\vec{E}$ must be along $z$. The sign of the $t$ term changes for direction consistency relative to the wave propagation.
Step 4: Conclusion
The correct expression is $E_z = 60 \sin(0.5 \times 10^3 x - 1.5 \times 10^{11} t)$.
Final Answer: (A)
Electromagnetic wave properties: $E_0 = c B_0$, wave travels in direction of $\vec{E} \times \vec{B}$.
Step 2: Meaning
$E_0 = 3 \times 10^8 \times 2 \times 10^{-7} = 60$ V/m.
Step 3: Analysis
Since $\vec{B}$ is along $y$ and wave propagates along $-x$, $\vec{E}$ must be along $z$. The sign of the $t$ term changes for direction consistency relative to the wave propagation.
Step 4: Conclusion
The correct expression is $E_z = 60 \sin(0.5 \times 10^3 x - 1.5 \times 10^{11} t)$.
Final Answer: (A)
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