A proton and an electron are initially at rest at a distance of 9 x 10^(-1) m. what will be their initial acceleration due to electric force that they exert on each other?
Answers
Answer:
By the end of this section, you will be able to:
State Coulomb’s law in terms of how the electrostatic force changes with the distance between two objects.
Calculate the electrostatic force between two charged point forces, 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.

Figure 1. 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
F=k∣q1q2∣r2F=k∣q1q2∣r2
Coulomb’s law calculates the magnitude of the force F between two point charges, q1 and q2, separated by a distance r. In SI units, the constant k is equal to
k=8.988×109N⋅m2C2≈8.99×109N⋅m2C2k=8.988×109N⋅m2C2≈8.99×109N⋅m2C2
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 Figure 2).
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 (F∝1r2)(F∝1r2) to an accuracy of 1 part in 1016. No exceptions have ever been found, even at the small distances within the atom.

Figure 2. The magnitude of the electrostatic force F between point charges q1 and q2 separated by a distance r 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 q1 is equal in magnitude and opposite in direction to the force it exerts on q2. (a) Like charges. (b) Unlike charges.
EXAMPLE 1. HOW STRONG IS THE COULOMB FORCE RELATIVE TO THE GRAVITATIONAL FORCE?
Compare the electrostatic force between an electron and proton separated by 0.530 × 10−10 m with the gravitational force between them. This distance is their average separation in a hydrogen atom.
Strategy
To compare the two forces, we first compute the electrostatic force using Coulomb’s law, F=k∣q1q2∣r2F=k∣q1q2∣r2. We then calculate the gravitational force using Newton’s universal law of gravitation. Finally, we take a ratio to see how the forces compare in magnitude.
Solution
Entering the given and known information about the charges and separation of the electron and proton into the expression of Coulomb’s law yields
F=k∣q1
Explanation:
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Explanation:
First you need to get the magnitude of the electric force using the formula: FE= k(q1 q2)/ r^2. Afterwards, you need to use the magnitude of electric force and use it to the second formula. F= ma where F is the magnitude of electric force and m are the mass of protons and electrons and a for acceleration. You must separate the solution for protons and electrons initial acceleration.