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 then find direction of Electric and Magnetic field?

Question

Answer

Understanding the Direction of Electric and Magnetic Fields
In a plane polarized electromagnetic wave propagating in a vacuum, the relationships between the electric field (E) and the magnetic field (B) can be analyzed using Maxwell's equations.

Wave Propagation Direction
- The wave propagates in the z-direction. This is typically represented as:
- E = E₀ cos(kz - ωt) in the x-direction
- B = B₀ cos(kz - ωt) in the y-direction

Derivatives Explained
- The derivatives of the electric field (E) and magnetic field (B) indicate their spatial and temporal relationships:
- ∂E/∂x = 0 and ∂E/∂y = 0: This implies that the electric field does not vary in the x and y directions, confirming a uniform plane wave.
- ∂B/∂x = 0 and ∂B/∂y = 0: Similarly, the magnetic field remains constant in the x and y directions.

Key Relationships
- The relationships indicate:
- ∂E/∂z = -∂B/∂t: This signifies that the change in the electric field in the z-direction correlates negatively with the change in the magnetic field over time.
- ∂B/∂z = +∂E/∂t: This indicates that the change in the magnetic field in the z-direction correlates positively with the change in the electric field over time.

Conclusion: Direction of Fields
- From the above relationships:
- The electric field (E) is oriented in the x-direction.
- The magnetic field (B) is oriented in the y-direction.
Thus, for an electromagnetic wave traveling in the z-direction, the electric field is perpendicular to the magnetic field, and both are perpendicular to the direction of wave propagation.

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