Radio Broadcast Antenna Peak Intensity

[Minescrushessouls]

Homework Statement

A radio broadcast antenna is located at the top of a steep tall mountain. The antenna is broadcasting 104.3 FM (in Megahertz) with a power of 5.00 kilowatts.

What is the peak intensity of the signal at a receiving antenna located 25.0 km away?

Homework Equations

Honestly, I don't really know

Intensity=P/d^2

Peak Intensity=some vector/μ₀

The Attempt at a Solution

So I tried doing 5000/(25000^2)

The power divided by the distance squared. The system told me my units were incorrect...so I guess I don't even know where to start on this

 

[Ugnius]

You should use equation of Poynting vector

 

[Minescrushessouls]

You should use equation of Poynting vector

Ok so S=(ExB)/μ

But how would I find E and B from the information provided?

 

[gneill]

Intensity is measured in watts per square meter. Think of the radio antenna as putting out 5 kW in a spherical distribution. At some distance R from the transmitter, what's the size of the spherical "surface"?

 

[Minescrushessouls]

So the area would be the area of a circle, or pi*r^2

So would that mean it would be W/(pi*r^2)?

 

[gneill]

So the area would be the area of a circle, or pi*r^2

So would that mean it would be W/(pi*r^2)?

No, the surface of a sphere is not a circle -- it's a spherical shell. What's the surface area of a spherical shell?

 

[Minescrushessouls]

No, the surface of a sphere is not a circle -- it's a spherical shell. What's the surface area of a spherical shell?

4*pi*r^2?

 

[gneill]

4*pi*r^2?

Yes.