Engineering College

The Magnetic Field of a plane wave traveling in the air is given by H=X 50 sin (2π x 10 ^7 -ky) (ma/m) determine the power density carried by the wave

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Answer 1

The power density carried by the wave is then given by the magnitude of the time-averaged Poynting vector Power Density (P) = |S|

If you have the values for X, E0, and k, please provide them, and I will be able to assist you further in calculating the power density carried by the wave.

To determine the power density carried by the plane wave, we need to calculate the time-averaged Poynting vector. The Poynting vector represents the flow of electromagnetic energy per unit area and is given by the cross product of the electric field and magnetic field vectors.

In this case, the given magnetic field is H = X50 sin(2πx10^7 - ky) (mA/m), where X is the polarization constant, k is the wave number, and y represents the direction perpendicular to the wave propagation.

Let's assume that the electric field vector is E = E0 sin(2πx10^7 - ky), where E0 is the amplitude of the electric field.

The time-averaged Poynting vector (S) can be calculated as:

S = (1/2) * Re(E x H*)

where Re represents the real part of the complex number and H* denotes the complex conjugate of the magnetic field.

The power density carried by the wave is then given by the magnitude of the time-averaged Poynting vector:

Power Density (P) = |S|

To compute the power density, we need the values of X, E0, and k. However, these values are not provided in the given information. Without these values, it is not possible to determine the exact power density carried by the wave.

If you have the values for X, E0, and k, please provide them, and I will be able to assist you further in calculating the power density carried by the wave.

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