Electric field amplitude question regarding intensity calculations

[MeatComet]

Homework Statement

A wireless telephone is emitting a constant 10,0mW effect in a homogenous area around the telephone. What is the amplitude of the electrical field 4,0cm from the headset?

Relevant Equations

I=P/A,
I=P/(4*pi*r^2),
I=P/(pi*r^2),

I=(1/2)*√(ε0/μ0)*(E0^2)

My question is specifically with calculating the intensity. The book solution is

I=P/(4*pi*r^2)

but would this not give me a weaker electrical amplitude in the final calculation after plugging it in to
I=(1/2)*√(ε₀/μ₀)*(E₀²) ?

 

[kuruman]

but would this not give me a weaker electrical amplitude in the final calculation after plugging it in to
I=(1/2)*√(ε₀/μ₀)*(E₀²) ?

Weaker than what? You are asked the find the amplitude at 4.0 cm from the headset.

 

[MeatComet]

Yes, and that would be the radius in I=P/(4*π*r²), but my question is why there is an extra 4 in the divider, does that not make it so that i only look at the quarter circle and would that imply that the book answer is only looking at the edge of the phone that is touching the face or somesuch?
Because if you only look at the area of the circle the antenna makes, that gives
A=π*r²
=>A=π*4²
But according to my book, they do
I=P/A=>
I=1/4*(P/(π*4²))
Which is, in fact, cutting the intensity of the field in 4, essentially only looking at a quarter slice?
Because as i understand the equation, the intensity is spread across a circular area, and to find the amplitude at 4.0cm you plug in the intensity per square centimeter across the field that you want, no?

 

[berkeman]

why there is an extra 4 in the divider

What is the surface area of a sphere?

 

[MeatComet]

AAAAAAAAAAAAAAAAAAAAAAARRRRRGGGGGGHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
Thanks man, i was looking at a circle. Why, why why why. Hahah, wish i could more than like your answer.