Measurement of electric field and magnetic field in a plane polarised electron magnetic wave in vacuum lead to the following result in which derivative of electric field with respect to X and y is given and derivative of magnetic field municipal to X and y is zero but derivative of electric field with respect to z is equal to negative of derivative of magnetic field with respect to time and derivative of magnetic field with respect to z is equals to positive of electric field with respect to time?

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Answer

Understanding Plane Polarized Electromagnetic Waves
In vacuum, plane polarized electromagnetic waves consist of oscillating electric (E) and magnetic (B) fields that are perpendicular to each other and to the direction of wave propagation. The derivatives of these fields provide insights into their behavior.

Key Observations
- **Electric Field Derivative**:
- The derivative of the electric field with respect to x and y is indicative of the fields oscillating in a plane.
- **Magnetic Field Derivative**:
- The derivative of the magnetic field with respect to x and y being zero suggests that the magnetic field does not vary in those directions.

Field Relationships
- **E and B Fields**:
- The relationship where the derivative of the electric field with respect to z is equal to the negative of the derivative of the magnetic field with respect to time indicates a coupling between the fields as they propagate.
- **Time Derivatives**:
- The derivative of the magnetic field with respect to z being equal to the positive of the electric field with respect to time shows that changes in the electric field generate changes in the magnetic field. This is fundamentally described by Maxwell's equations, particularly Faraday's Law of Induction.

Conclusion
These relationships illustrate the interdependence of electric and magnetic fields in electromagnetic waves. The oscillations of the electric field create magnetic fields and vice versa, maintaining the wave's propagation through space. Understanding these dynamics is crucial for applications in optics, telecommunications, and various electromagnetic technologies.

Similar Physics Doubts

An electromagnetic wave whose electric field is given belowEz= 0

In a non-magnetic dielectric medium with dielectric constant = 4, the electric field of a propagating plane wave with omega= 10^8 rad/s is given by. E = (-i+√3j) exp[j(omega.t-k.r)] The propagation vector k is given by?

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