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 find direction of electric field and magnetic field show with proper calculation?

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Answer

Introduction
In a plane polarized electromagnetic wave propagating in vacuum, the electric field (**E**) and magnetic field (**B**) have specific relationships governed by Maxwell's equations.

Field Derivatives
- Given conditions:
- ∂E/∂x = ∂E/∂y = 0
- ∂B/∂x = ∂B/∂y = 0
- ∂E/∂z = -∂B/∂t
- ∂B/∂z = ∂E/∂t
These equations indicate that both fields are uniform in the x and y directions, and vary in the z direction as functions of time (t).

Direction of Propagation
For a plane polarized wave propagating in the z-direction, the electric and magnetic fields are perpendicular to each other and to the direction of propagation.
Using the right-hand rule:
- If **E** is in the x-direction, then **B** will be in the y-direction.
- The direction of wave propagation (z) is given by **E** × **B**.

Field Vector Relationships
Assuming:
- **E** = E₀ **i** (where **i** is the unit vector in the x-direction)
- **B** = B₀ **j** (where **j** is the unit vector in the y-direction)
Using the relationships derived earlier, we find:
- From ∂E/∂z = -∂B/∂t: This shows how **E** changes with z is related to the change of **B** with time.
- From ∂B/∂z = ∂E/∂t: This shows how **B** changes with z is related to the change of **E** with time.

Conclusion
Thus, in a plane polarized electromagnetic wave:
- The **E** field is directed along the x-axis.
- The **B** field is directed along the y-axis.
- The wave propagates in the z-direction, confirming the orthogonal relationship between the fields and the direction of propagation.

Similar Physics Doubts

A beam of plane-polarized light falls on a polarizer which rotates about the axis of the ray with angular velocity ω = 22 rad/sec. Find the energy (mJ) of light passing through the polarizer per one revolution if the flux of energy of the incident ray is equal to φ = 14 mω.

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