A magnetic field vector in an electromagnetic wave is represented by B = B0 sin (2πvt - 2πx/λ) j. Its associated electric field vector is _________.

The correct answer is Option 1. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q40 – JEE-MAIN 2026

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Home Physics EM WavesQuestion #166

A magnetic field vector in an electromagnetic wave is represented by

\vec{B} = B_{0} \sin (2 π ν t - \frac{2 π x}{λ}) \hat{j}

Its associated electric field vector is _________.

Clue 1 of 3: Properties of EM Waves

In a plane electromagnetic wave, the electric field, magnetic field, and direction of propagation are mutually perpendicular.

🧠 Full Solution Path

Step 1: Determine Wave Propagation Direction and E-field Direction✦ Active

The given magnetic field is $\vec{B} = B_{0} \sin (2 π ν t - \frac{2 π x}{λ}) \hat{j}$ . The term $(2 π ν t - \frac{2 π x}{λ})$ indicates that the wave is propagating in the positive x-direction (along $\hat{i}$ ). The magnetic field oscillates along the y-axis (along $\hat{j}$ ). For an electromagnetic wave, the electric field $\vec{E}$ , magnetic field $\vec{B}$ , and propagation direction $\vec{k}$ are mutually perpendicular. The direction of propagation is given by $\vec{S} \propto \vec{E} \times \vec{B}$ . Since $\vec{S}$ is along $\hat{i}$ and $\vec{B}$ is along $\hat{j}$ , we need $\vec{E} \times \hat{j} = \hat{i}$ . This implies that $\vec{E}$ must be along $- \hat{k}$ because $(- \hat{k}) \times \hat{j} = - (\hat{k} \times \hat{j}) = - (- \hat{i}) = \hat{i}$ .

💡 Teacher's Secret Hint

Remember the right-hand rule for cross products and the relationship between E, B, and propagation direction.

Step 2: Determine the Amplitude of the Electric Field○ Expand

The amplitudes of the electric and magnetic fields in an electromagnetic wave are related by $E_{0} = c B_{0}$ , where $c$ is the speed of light in vacuum. The speed of light can also be expressed as $c = ν λ$ , where $ν$ is the frequency and $λ$ is the wavelength. Substituting this into the amplitude relation, we get $E_{0} = (ν λ) B_{0}$ .

💡 Teacher's Secret Hint

Ensure you use the correct relationship between the speed of light, frequency, and wavelength.

Step 3: Construct the Electric Field Vector○ Expand

The electric field oscillates in phase with the magnetic field. Combining the amplitude $E_{0} = ν λ B_{0}$ , the phase term $\sin (2 π ν t - \frac{2 π x}{λ})$ , and the direction $- \hat{k}$ , the electric field vector is:

\vec{E} = - ν λ B_{0} \sin (2 π ν t - \frac{2 π x}{λ}) \hat{k}

This matches option 1.

💡 Teacher's Secret Hint

The phase of the electric and magnetic fields in an EM wave is the same.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 40 – JEE-MAIN 2026

Clue 1 of 3: Properties of EM Waves

🧠 Full Solution Path