Newton’s law of gravitation and Coulomb’s law
Two force laws with the same shape: both fall off as 1 / r². Then the field of a point source.
In a hydrogen atom the electron and proton attract each other twice over: by gravity AND by electric force. Which one actually holds the atom together?
The distance between two point masses is tripled. The gravitational force between them becomes…
Two small charged spheres repel each other with a force F. One sphere’s charge is doubled and the distance between them is also doubled. The new force is…
At the surface of the Earth g = 9.8 N kg⁻¹. At a height equal to one Earth radius above the surface, g is about…
A point charge of 2.0 μC is fixed in place. The electric field strength 0.20 m from it is about…
Why is gravity NOT the main force holding an electron in an atom?
The Earth and the Moon are huge, yet we use F = G M m / r² with r = 3.84 × 10⁸ m. Explain why this is allowed, and what r means.
Which field does a moving charge create, in addition to the others?
The direction of an electric field is the direction of the force on…
Key points
- • F_G = GMm / r² always attracts. F_E = kQq / r² attracts unlike and repels like charges.
- • Both fall off as 1 / r². Double the distance and the force (and field) is a quarter.
- • g = GM / r² and E = kQ / r². The test object cancels.
- • For a sphere, r is measured from the centre.
Formulas
- FG = G M m / r²
- FE = k Q q / r²
- g = G M / r²
- E = k Q / r²
Key terms
- Point mass :
- an object much smaller than the distances involved
- Inverse-square law :
- a quantity proportional to 1 / r²
Common errors
- • Using the height above the surface as r instead of the distance to the centre.
- • Forgetting to square r.
- • Using the signs of the charges as part of the magnitude of F.