Measurement of electric field and magnetic field B in a plane polarise light wave in vacuum lead to following in which derivative of electric field with respect to X and y is zero derivative of magnetic field with respect to X and y is zero derivative of electric field with respect to z is equal to minus del b by delta and derivative of magnetic field B with respect to z is equals to positive Dell e by delta?

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Answer

Understanding Electromagnetic Waves in Vacuum
In a plane polarized light wave propagating in a vacuum, the electric field (E) and magnetic field (B) exhibit specific spatial relationships defined by Maxwell's equations. The derivatives of these fields with respect to spatial coordinates reveal their fundamental properties.

Key Properties of Electric and Magnetic Fields
- The derivatives of the electric field with respect to **x** and **y** are **zero**:
- This indicates that the electric field is uniform in the plane perpendicular to the direction of wave propagation (z-direction).
- The derivatives of the magnetic field with respect to **x** and **y** are **zero**:
- Similar to the electric field, this shows that the magnetic field is also uniform in the same plane.

Relationship Between Fields in the z-Direction
- The derivative of the electric field with respect to **z** is equal to **−∂B/∂t**:
- This relationship signifies that a change in the electric field in the direction of propagation is related to the rate of change of the magnetic field. This is a manifestation of Faraday's law of induction.
- The derivative of the magnetic field with respect to **z** is equal to **+∂E/∂t**:
- This indicates that a change in the magnetic field in the propagation direction corresponds to the rate of change of the electric field, demonstrating the interdependence of the two fields as described by Maxwell’s equations.

Conclusion
The interrelation between the electric and magnetic fields in a plane polarized light wave elucidates the wave nature of electromagnetic radiation, where changes in one field induce changes in the other, allowing for the propagation of energy through space. This is a fundamental concept in electromagnetism and is crucial for understanding light behavior.

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