Sunlight, Intensity, electric field RMS

[ooohffff]

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=cε_oE_rms²
E=V/d

The Attempt at a Solution

E_earth=V/d
Since Uranus is 19.2 times farther away then:
E_uranus=E_earth/19.2

I_earth = 1350 W/m²
I_earth=cε_oE_{earth rms}²
E_{uranus rms} = E_{earth rms} / 19.2 = √ ( I / (cε_o)) / 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!

 

[TJGilb]

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.

 

[TJGilb]

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.

 

[ooohffff]

Thanks! I got it right :)