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

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

Physics Q9 – NEET-UG 2025

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Home Physics EM WavesQuestion #168

The electric field in a plane electromagnetic wave is given by

E_{z} = 60 \cos (5 x + 1.5 \times 10^{9} t) V / m

. Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field) :

Clue 1 of 3: Relationship between E and B fields

In a plane electromagnetic wave, the electric field ( $\vec{E}$ ), magnetic field ( $\vec{B}$ ), and the direction of wave propagation ( $\vec{k}$ ) are mutually perpendicular.

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Step 1: Extract Parameters and Determine Wave Direction✦ Active

The given electric field is $E_{z} = 60 \cos (5 x + 1.5 \times 10^{9} t) V / m$ . From this equation, we can identify the following:

- The amplitude of the electric field is $E_{0} = 60 V / m$ .

- The wave number is $k = 5 rad/m$ and the angular frequency is $ω = 1.5 \times 10^{9} rad/s$ .

- The argument $(k x + ω t)$ indicates that the wave propagates along the negative x-direction (i.e., $\vec{k}$ is along $- \hat{i}$ ).

- The electric field is along the z-axis (i.e., $\vec{E}$ is along $\hat{k}$ ).

Step 2: Calculate the Amplitude of the Magnetic Field○ Expand

In an electromagnetic wave, the amplitudes of the electric and magnetic fields are related by the speed of light $c$ . The speed of light in vacuum is $c = 3 \times 10^{8} m/s$ .

E_{0} = c B_{0} ⟹ B_{0} = \frac{E_{0}}{c}

Substituting the values:

B_{0} = \frac{60 V/m}{3 \times 10^{8} m/s} = 20 \times 10^{- 8} T = 2 \times 10^{- 7} T

💡 Teacher's Secret Hint

Remember the fundamental relationship between the amplitudes of E and B fields in an EM wave.

Step 3: Determine the Direction and Phase of the Magnetic Field○ Expand

The electric field ( $\vec{E}$ ), magnetic field ( $\vec{B}$ ), and the direction of wave propagation ( $\vec{k}$ ) are mutually perpendicular. Their directions are related by the right-hand rule: $\vec{k} = \vec{E} \times \vec{B}$ .

We have $\vec{E}$ along $\hat{k}$ (z-axis) and $\vec{k}$ along $- \hat{i}$ (negative x-axis). We need to find $\vec{B}$ such that $\hat{k} \times \vec{B} = - \hat{i}$ .

Using the cross product rules, $\hat{k} \times \hat{j} = - \hat{i}$ . Therefore, $\vec{B}$ must be along the y-axis ( $\hat{j}$ ).

Also, the electric and magnetic fields in an electromagnetic wave oscillate in phase. This means they share the same functional form (cosine) and argument $(5 x + 1.5 \times 10^{9} t)$ .

Combining the amplitude, direction, and phase, the expression for the magnetic field is:

B_{y} = B_{0} \cos (5 x + 1.5 \times 10^{9} t) = 2 \times 10^{- 7} \cos (5 x + 1.5 \times 10^{9} t) T

Comparing this with the given options, option (1) matches our derived expression.

💡 Teacher's Secret Hint

Visualize the coordinate system and apply the right-hand rule carefully for the cross product $\vec{E} \times \vec{B}$ .

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Physics Question 9 – NEET-UG 2025

Clue 1 of 3: Relationship between E and B fields

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