Sunlight, Intensity, electric field RMS

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SUMMARY

The discussion focuses on calculating the root mean square (RMS) electric field in sunlight reaching Uranus, given that Earth receives approximately 1350 W/m² and Uranus is 19.2 times farther from the Sun. The formula used is I = cε₀Eₗₘₛ², leading to the conclusion that the RMS electric field at Uranus is approximately 37.14 V/m. A participant confirmed this calculation, noting a slight variation to 37.15 V/m, emphasizing the importance of understanding the relationship between electric potential and field strength.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically electric fields and potentials.
  • Familiarity with the concept of intensity in the context of electromagnetic radiation.
  • Knowledge of the constants involved in electromagnetic equations, such as c (speed of light) and ε₀ (permittivity of free space).
  • Ability to manipulate equations involving RMS values and distances in physics.
NEXT STEPS
  • Study the derivation of the relationship between intensity and electric field strength in electromagnetic waves.
  • Learn about the implications of distance on electric field strength in the context of inverse square laws.
  • Explore the concept of electric potential gradients and their relation to electric fields.
  • Investigate the differences between RMS values and peak values in alternating current (AC) circuits.
USEFUL FOR

Students and professionals in physics, particularly those focusing on electromagnetism, as well as educators looking to enhance their understanding of electric fields in astrophysical contexts.

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Homework Statement


Estimate the rms electric field in the sunlight that hits Uranus, knowing that the Earth receives about 1350 W/m2 and that Uranus is 19.2 times farther away from the Sun (on average) than is the Earth.

Homework Equations


I=cεoErms2
E=V/d

The Attempt at a Solution


Eearth=V/d
Since Uranus is 19.2 times farther away then:
Euranus=Eearth/19.2

Iearth = 1350 W/m2
Iearth=cεoEearth rms2
Euranus rms = Eearth rms / 19.2 = √ ( I / (cεo)) / 19.2
= 37.14 V/m

I got this problem wrong several times so I just wanted to verify that I did it right this time. Thanks!
 
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Be aware that saying the electric field is equal to the electric potential divided by distance implies that you are assuming a constant electric field. In actuality the electric field equals the negative gradient of the potential.
 
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But yes, that answer does look right. I just calculated it using the relation between power and intensity, calculating the intensity for a distance 19.2 times greater, and plugging into your equation, and I came out with 37.15 V/m.
 
Thanks! I got it right :)
 

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