Dipoles and Radiated power

In summary, the power radiated by the system can be calculated using the formula P_{rad}=\frac{μω^{4}p^{2}}{12πc}, where p is the total dipole moment of the system. The individual x and y components of the dipoles can be added together to find the total dipole moment, as they are orthogonal. The given equations and approach are correct and can be used to solve for P_{rad}.
  • #1
atomqwerty
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Homework Statement



We have the setup shown in the figure (see http://cl.ly/JGDDfigure). It rotates with angular velocity ω counter clockwise. ¿Power radiated by the system? (Sorry if it's not the correct translation -- Potencia radiada in spanish).

Homework Equations



[itex]P_{rad}=\frac{μω^{4}p^{2}}{12πc}[/itex]

The Attempt at a Solution



The dipoles 1 and 2 can be written (module) as p=lq=√2q. Can be split in its x and y components:

Dipole 1

p_x = √2q cos (ωt + 45)
p_y = √2q sin (ωt + 45)

Dipole 2

p_x = √2q cos (ωt - 45)
p_y = √2q sin (ωt - 45)

Dipole 3 (given)

p_y = p sin (ωt + 90)

Now, since they do not interfiere between them (orthogonal), we can write

[itex]p^{2} = p^{2}_{x} + p^{2}_{y}[/itex]

in the equation for P.

Is this correct? Thanks!
 
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  • #2


Hello! Yes, your approach and equations are correct. The power radiated by the system can be calculated using the formula P_{rad}=\frac{μω^{4}p^{2}}{12πc}, where p is the total dipole moment of the system. Since the dipoles are orthogonal, we can calculate the total dipole moment by adding the individual x and y components squared. So, your equation for p^{2} is correct. You can then plug in the values for p^{2} and solve for P_{rad}. Let me know if you have any further questions. Good luck!
 

What is a dipole?

A dipole is a type of antenna that consists of two conductive elements, typically metal rods, that are separated by a small distance. It is a fundamental element in many types of radio communication systems, including AM and FM radio, television, and cellular networks.

How does a dipole radiate power?

A dipole radiates power by creating a changing electric field between its two conductive elements. As an alternating current flows through the dipole, the electric field oscillates, creating electromagnetic waves that propagate outward into space.

What is the difference between a half-wave and a quarter-wave dipole?

A half-wave dipole is a dipole antenna whose total length is equal to half the wavelength of the radio frequency it is designed to transmit or receive. A quarter-wave dipole is half the length of a half-wave dipole and is typically used in applications where a smaller antenna size is necessary.

How is the direction of radiation determined in a dipole antenna?

The direction of radiation in a dipole antenna is determined by the orientation of the conductive elements. The strongest radiation occurs perpendicular to the direction of the elements, while little to no radiation occurs along the axis of the elements.

What factors affect the radiated power of a dipole antenna?

The radiated power of a dipole antenna is affected by several factors, including the length and diameter of the conductive elements, the frequency of the electromagnetic waves, and the surroundings of the antenna. Additionally, the efficiency of the antenna, which is influenced by materials and construction, also plays a role in the radiated power.

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