What is the earths net charge?

Question

The intensity of the earths electric field near its surface is 130 N/C pointing down. What is the earth's net charge? Assuming that this field is caused by it (Use gauss's law)

Answer 1

Using Randy's answer with E for the electric field,

 

Q = ε₀E4πR²

 

= (8.854 x 10^-12)(-130)4π(6.370 x 10⁶)² = -5.87 x 10⁵ C

Answer 2

Gauss's Law for Electricity tells us that the Flux across a closed surface of an Electric Field is proportional to its enclosed charge. Flux is the area of the surface times the strength of the field times cos(a) where a is the angle between the normal (perpendicular) to the surface and the field itself. In general, problems of this form require calculus, but because the field is always perpendicular to the surface of Earth, none is required, and the flux is simply F*SA where F is the given field strength and SA is the surface area of a sphere.

 

In Symbols,

 

Flux=F*SA (Definition of Flux)

 

Flux=Q/e (Gauss's Law)

 

SA= 4pi*R^2 (Surface Area of Sphere)

 

Putting it all together,

 

Q=e*Flux (note e is the permittivity of free space)

 

Q=e*F*SA

 

Q=e*f*4pi*R^2

 

Now we have an expression for Charge in terms of experimentally determined and given constants -- substitute their values and you have your answer!