What Charge Must a Wooden Sphere Have to Float Above the Earth?

[Numeriprimi]

Hello, everyone :-)

We have a wooden sphere at a height of h = 1 m above the surface of the Earth which has a perimeter of RZ = 6 378 km and a weight of MZ = 5.97 · 10^24 kg. The sphere has a perimeter of r = 1 cm and is made of a wood which has the density of ρ = 550 kg·m − 3. Assume that the Earth has an electric charge of Q = 5 C. What is the charge q that the sphere has to have float above the surface of the Earth? How does this result depend on the height h?

We can use Coulomb's and Newton's law.

I can say the force of F = m_s*g = 4/3 * π * r^3 * ρ * g = the force of Coulomb's law
4/3*π*r^3*ρ*g = |Q_1|*|Q_2|/(4*π*e_0*e_1)
|Q_1| = 4/3*π*r^3*ρ*g*4*π*e_0*e_1/|Q_2|

Ok, this is my solution. Is it OK?
Sorry for my bad English and thanks for advice.

 

[Simon Bridge]

Hello, everyone :-)

We have a wooden sphere at a height of h = 1 m above the surface of the Earth which has a perimeter of RZ = 6 378 km

I take it English is a second language. Here, let me help...
A 'perimeter" is something a 2D surface may have - something you could put a fence around.
6378km is the radius of the Earth.
1cm is the radius of the wooden sphere.

and a weight of MZ = 5.97 · 10^24 kg.

That would be the mass of the Earth - "weight" is the force of gravity.
Weight is sometimes given in mass units for objects close to the surface of the Earth.

The sphere has a perimeter of r = 1 cm and is made of a wood which has the density of ρ = 550 kg·m − 3. Assume that the Earth has an electric charge of Q = 5 C. What is the charge q that the sphere has to have float above the surface of the Earth? How does this result depend on the height h?

I can say the force of F = m_s*g = 4/3 * π * r^3 * ρ * g = the force of Coulomb's law
4/3*π*r^3*ρ*g = |Q_1|*|Q_2|/(4*π*e_0*e_1)
|Q_1| = 4/3*π*r^3*ρ*g*4*π*e_0*e_1/|Q_2|

It helps if you write down your reasoning.
I'll have to see what I can deduce from what you wrote.

4/3*π*r^3*ρ*g = |Q_1|*|Q_2|/(4*π*e_0*e_1)

$\frac{4}{3}\pi r^3\rho g$ is the weight of the wooden sphere in the approximation that h<<RZ ... which would be good.

You are reasoning that the coulomb force must be equal and opposite to this?

$\frac{Q_1 Q_2}{4\pi\epsilon_0\epsilon_1}$[/size]... is not the coulomb force.

Lets have q on the wooden sphere and Q on the Earth.
How far away is the charge Q from the charge q?
How does the force between two charges depend on the distance between them?
What is $\epsilon_1$ for?