State Coulomb's law in terms of how the electrostatic force changes with the distance between two objects.
Calculate the electrostatic force between two point charges, such as electrons or protons.
Compare the electrostatic force to the gravitational attraction for a proton and an electron; for a human and the Earth.
The information presented in this section supports the following AP® learning objectives and science practices:
3.A.3.3 The student is able to describe a force as an interaction between two objects and identify both objects for any force.
(S.P. 1.4)
3.A.3.4 The student is able to make claims about the force on an object due to the presence of other objects with the same property: mass, electric charge.
(S.P. 6.1, 6.4)
3.C.2.1 The student is able to use Coulomb's law qualitatively and quantitatively to make predictions about the interaction between two electric point charges (interactions between collections of electric point charges are not covered in Physics 1 and instead are restricted to Physics 2).
(S.P. 2.2, 6.4)
3.C.2.2 The student is able to connect the concepts of gravitational force and electric force to compare similarities and differences between the forces.
(S.P. 7.2)
This NASA image of Arp 87 shows the result of a strong gravitational attraction between two galaxies. In contrast, at the subatomic level, the electrostatic attraction between two objects, such as an electron and a proton, is far greater than their mutual attraction due to gravity. (credit: NASA/HST)
Through the work of scientists in the late 18th century, the main features of the
electrostatic force —the existence of two types of charge, the observation that like charges repel, unlike charges attract, and the decrease of force with distance—were eventually refined, and expressed as a mathematical formula. The mathematical formula for the electrostatic force is called
Coulomb's law after the French physicist Charles Coulomb (1736–1806), who performed experiments and first proposed a formula to calculate it.
Coulomb's law
Coulomb's law calculates the magnitude of the force
between two point charges,
and
, separated by a distance
. In SI units, the constant
is equal to
The electrostatic force is a vector quantity and is expressed in units of newtons. The force is understood to be along the line joining the two charges. (See
[link] .)
Although the formula for Coulomb's law is simple, it was no mean task to prove it. The experiments Coulomb did, with the primitive equipment then available, were difficult. Modern experiments have verified Coulomb's law to great precision. For example, it has been shown that the force is inversely proportional to distance between two objects squared
to an accuracy of 1 part in
. No exceptions have ever been found, even at the small distances within the atom.
The magnitude of the electrostatic force
between point charges
and
separated by a distance
is given by Coulomb's law. Note that Newton's third law (every force exerted creates an equal and opposite force) applies as usual—the force on
is equal in magnitude and opposite in direction to the force it exerts on
. (a) Like charges. (b) Unlike charges.
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
