Dipole Radiation Homework: Amplitude & Direction at P2, Total Power

[Josephk1508]

Homework Statement

Given a Electric dipole located at the origin of the coordinate system, which oscillates with a given frequency and amplitude, creating an electromagnetic wave. It is found that no power can be detected at point P1 = (3 y) m (i.e. the intensity of the wave at that point is zero). Another measurement is made at the point P2 = (1 x) m where it is found that the radiation is locally a plane monochromatic wave.

Homework Equations

Poynting's vector is <S> = 2.5 x J/m^2s

The Attempt at a Solution

I solved the first part but stuck when it asks me Find the amplitude and direction of oscillation of E and B at P2? And the total power radiated by the dipole? The total power emitted is calculated by using the flux of <S> crossing a spherical surface radius r, but still finding it tricky.

 

[mark726]

Thank you for your post. It seems like you have made some progress in solving the first part of the problem. To find the amplitude and direction of oscillation of E and B at P2, you can use the fact that the radiation at this point is a plane monochromatic wave. This means that the electric and magnetic fields at this point are perpendicular to each other and the direction of propagation. The direction of propagation can be found using the direction of the Poynting vector, which is given as <S> = 2.5 x J/m^2s. This means that the direction of propagation is in the positive x-direction.

To find the amplitude of the fields, you can use the relationship between the Poynting vector and the amplitude of E and B, given by <S> = 1/2 * c * ε0 * E0^2. Here, c is the speed of light and ε0 is the permittivity of free space. You know the value of <S>, so you can solve for E0. Since the radiation is a plane monochromatic wave, the amplitude of E and B will be the same, so you can use this value for both.

Once you have found the amplitude and direction of E and B, you can use the formula for the total power emitted by the dipole, given by P = 1/2 * ε0 * c * E0^2 * A, where A is the surface area of the sphere with radius r. You can use this formula to find the total power radiated by the dipole.

I hope this helps you solve the rest of the problem. Good luck!