1. B_y = 2×10⁻⁷cos(5x+1.5×10⁹ t)T 2. B_x = 2×10⁻⁷cos(5x+1.5×10⁹ t)T 3. B_z = 60cos(5x+1.5×10⁹ t)T 4. B_y = 60sin(5x+1.5×10⁹ t)T

Answer: 1. B_y = 2×10⁻⁷cos(5x+1.5×10⁹ t)T Key idea: in an EM wave, B₀=E₀/c , and vec E×vec B points along the direction of propagation. The argument 5x+1.5×10⁹t means the wave travels in the -x direction, with c=ω/k=1.5×10⁹/5=3×10⁸ m/s. B₀=E₀/c=frac603×10⁸=2×10⁻⁷\ mathrm T Direction: E is along z and propagation is along -x . Since hat z×hat y=-hat x , the magnetic field is along y . So B_y=2×10⁻⁷cos(5x+1.5×10⁹t) T. Option 3 has the wrong magnitude and direction, and option 4 has the wrong phase.

Topic: EM waves, characteristics and transverse nature· Electromagnetic Waves

The electric field in a plane electromagnetic wave is given by E_z = 60(5x + 1.5×10^9 t) V/m. Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field) :

1. $B_y = 2\times10^{-7}\cos(5x+1.5\times10^9 t)T$

2. $B_x = 2\times10^{-7}\cos(5x+1.5\times10^9 t)T$

3. $B_z = 60\cos(5x+1.5\times10^9 t)T$

4. $B_y = 60\sin(5x+1.5\times10^9 t)T$

Doubtly Asked 30 Oct 2026 NEET UG 2025 Practice test neet Save WhatsApp Report

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Answer: 1. $B_y = 2\times10^{-7}\cos(5x+1.5\times10^9 t)T$

Key idea: in an EM wave, $B_0=E_0/c$, and $\vec E\times\vec B$ points along the direction of propagation.

The argument $5x+1.5\times10^{9}t$ means the wave travels in the $-x$ direction, with $c=\omega/k=\dfrac{1.5\times10^9}{5}=3\times10^{8}$ m/s.

$$B_0=\frac{E_0}{c}=\frac{60}{3\times10^{8}}=2\times10^{-7}\ \mathrm T$$

Direction: $E$ is along $z$ and propagation is along $-x$. Since $\hat z\times\hat y=-\hat x$, the magnetic field is along $y$. So $B_y=2\times10^{-7}\cos(5x+1.5\times10^9t)$ T. Option 3 has the wrong magnitude and direction, and option 4 has the wrong phase.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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The electric field in a plane electromagnetic wave is given by E_z = 60(5x + 1.5×10^9 t) V/m. Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field) :

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