Earth's charge and number of its electron per sq. meter

[Hooke's Law]

Homework Statement

The Earth is surrounded by an electric field, pointing inward at every point. Assume a magnitude of E = 167N/C near the surface. What is the net charge on the Earth?
How many excess electrons per square meter on the Earth's surface does this correspond to?

Homework Equations

E = kq/r^2

The Attempt at a Solution

In the first question I got an answer of -7.56E+05 C, but I don't know how to start with the 2nd one.

 

[gneill]

If you have the number of coulombs, and each electron has a charge of e- coulombs,...

If I may make a small suggestion, if you do the problem strictly symbolically (don't plug in any numbers until the very end) and you know that k = 1/(4 π ε_o), then you will amazed at how many things cancel out, and thus how many things you don't need to look up values for.

 

[Hooke's Law]

If you have the number of coulombs, and each electron has a charge of e- coulombs,...

If I may make a small suggestion, if you do the problem strictly symbolically (don't plug in any numbers until the very end) and you know that k = 1/(4 π ε_o), then you will amazed at how many things cancel out, and thus how many things you don't need to look up values for.

I got the net charge of the earth. Should I divide that charge by the charge of one electron ( -1.6022*10^-19) ? I tried it but it didnt work..

 

[gneill]

I got the net charge of the earth. Should I divide that charge by the charge of one electron ( -1.6022*10^-19) ? I tried it but it didnt work..

In what way did it not work? Did it not give you a figure for the total number of electrons?

 

[Hooke's Law]

n = total charge / electron charge = 4.71*10^24

The computer won't accept it, and did I do it right?

 

[gneill]

n = total charge / electron charge = 4.71*10^24

The computer won't accept it, and did I do it right?

You've done it right so far. You're not quite done yet! What precisely does the problem want you to find?

 

[Hooke's Law]

It's asking the number of excess electrons per square meter on the Earth's surface.

So I guess the value that I got in my previous post is the the number of electrons but not the excess ones, am I right? How do I find the excess electrons? Does "electrons per square meter" contribute to the problem?

Thanks

 

[gneill]

It's asking the number of excess electrons per square meter on the Earth's surface.

So I guess the value that I got in my previous post is the the number of electrons but not the excess ones, am I right? How do I find the excess electrons? Does "electrons per square meter" contribute to the problem?

Thanks

The number you calculated is the number of electrons in excess. You just haven't spread them out evenly over the surface of the Earth yet to find out how many fit per square meter.

 

[Hooke's Law]

So is there some integral needed? integral of the volume of the Earth(sphere)? from 0 to 1 where the numbers correspond the number of squares.

 

[gneill]

So is there some integral needed? integral of the volume of the Earth(sphere)? from 0 to 1 where the numbers correspond the number of squares.

The Earth is (to a good approximation) a sphere. What's the surface area of a sphere?