What Is the Charge on Earth Producing Its Electric Field?

[jrzygrl]

Homework Statement

Near the surface of the Earth there is an electric field with a magnitude of about 92 N/C directed vertically down. Assume this field is caused by a net free charge on the Earth.

(a) What are the magnitude and sign of the charge on the total Earth that produces this field?

Homework Equations

I tried using m_earth g / E but this not appear to yield the correct answer.

The Attempt at a Solution

mg / E
(5.9736 x 10²⁴ * -10) / 92
-6.49 x 10²³ C

Thanks for the help!

 

[Nabeshin]

I'm unsure as to why you're using the mass of the earth.

There is an object (the earth) causing an electric field to be generated with a magnitude 92N/C at the surface (distance known) from the center.

Perhaps try thinking about the problem as if the Earth were merely a particle located at the center.

 

[Defennder]

Why are you using mg here? This is for an electric field, not a gravitational field. The E-field is due entirely to the net charge and not the gravitational field. Just apply the formula for E-field due to a charge here, taking into account the radius of the Earth.