Physics Chapter: Coulomb's Law

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Questions and Answers

According to Coulomb's law, what happens when the distance between two point charges is halved?

The force between them quadruples (correct)

The force between them halves

The force between them doubles

The force between them remains unchanged

What is the unit of electrical charge in the S.I. system?

Coulomb (correct)

Ampere

Newton

Volt

What is the value of the permittivity of free space (ε₀) in S.I. units?

9 x 10⁹ N-m²/C

3 x 10⁸ C²/N-m²

8.85 x 10⁻¹² C²/N-m² (correct)

6.67 x 10⁻¹¹ N(m/kg)²

Which formula represents Coulomb's law in its scalar form for the force between two charges q₁ and q₂, separated by a distance r?

F = kq₁q₂/r² Signup and view all the answers

In Coulomb's law, the constant k is equal to which of the following?

1/4πε₀ Signup and view all the answers

What force will two charges of 1 C each at a distance of 1 m exert on each other?

9 x 10⁹ N Signup and view all the answers

What is the SI unit definition of a coulomb?

1 C = 1 A-s Signup and view all the answers

What is the force between two charges of +2 C and -3 C placed 2 meters apart in a vacuum?

4.5 x 10⁹ N Signup and view all the answers

What is the charge on a proton in terms of elementary charge?

+e Signup and view all the answers

How many electrons are needed to make up a charge of 1 Coulomb?

6 × 10^{18} electrons Signup and view all the answers

What is 1 microcoulomb (1 µC) equivalent to?

10^{-6} C Signup and view all the answers

Which of the following forces is stronger at separations of the order of 10^{-15} m or less in an atomic nucleus?

Nuclear forces Signup and view all the answers

What property of charge states that it is always an integral multiple of the elementary charge?

Quantization of charge Signup and view all the answers

What happens to the total charge in an isolated system over time?

It remains unchanged Signup and view all the answers

What is the charge on an object measured with respect to in scientific terms?

Elementary charge Signup and view all the answers

What is the main reason Coulomb's law fails to explain the stability of an atomic nucleus?

Existence of nuclear forces Signup and view all the answers

Which unit is typically used for measuring small values of electric charge?

Microcoulomb Signup and view all the answers

What unit is equivalent to 10^{-9} Coulombs?

Nanocoulomb (nC) Signup and view all the answers

Study Notes

Coulomb's Law

There are two types of electric charges: positive and negative.
Like charges repel each other, while unlike charges have mutual attraction.
The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The mathematical form of Coulomb's law is: F = kq₁q₂/r², where k is a constant.
In S.I. units, k is written as 1/4πε₀, where ε₀ is the permittivity of free space.
The value of ε₀ is 8.85 x 10⁻¹² C²/N-m² and that of 1/4πε₀ is 8.99 x 10⁹ N-m²/C or 9 x 10⁹ N-m²/C.

Vector Form of Coulomb's Law

The force F experienced by a point charge q₂ situated at a vector distance r from a point charge q₁ at the origin O is given by: F = (1/4πε₀) q₁q₂/r² * r̂.
The magnitude of each force is F = (1/4πε₀) q₁q₂/r².

Unit of Charge

In S.I. system, the unit of charge is coulomb (C) and is defined as the amount of charge that flows through a cross-section of a wire in 1 second if there is a steady current of 1 ampere in the wire.
1 coulomb (C) = 1 ampere-second (A-s).
An alternative definition of coulomb is: the amount of charge which when placed at a distance of 1 m from an equal and similar charge in vacuum, repels it with a force of 9 x 10⁹ newton.
The most fundamental unit of charge is the magnitude of charge on an electron or proton, denoted by e.

Electromagnetics

The charge on an electron is -e and that on a proton is +e, with e being a fundamental unit of charge that is very small.
A Coulomb represents the negative of the total charge of about 6 × 10^18 electrons, equivalent to a current of 1 ampere.
Typical values of charge range from about 10^(-6) C to 10^6 C, making microcoulomb (µC) and nanocoulomb (nC) units useful in measurements.
1 microcoulomb (1 µC) = 10^(-6) C and 1 nanocoulomb (1 nC) = 10^(-9) C.

Importance of Coulomb's Law

Coulomb's law applies to point charges, but can be extended to distributions of charges.
The law holds good over a wide range of distances, from 10^(-15) m to several kilometers.
Coulomb's law, combined with quantum theory, explains forces that bind:
- Electrons with the nucleus in an atom.
- Atoms to form a molecule.
- A large number of atoms or molecules to form liquids and solids.
The atomic nucleus, containing positively charged protons and uncharged neutrons, has a size of about 10^(-15) m.
Coulomb's law cannot account for the stability of an atomic nucleus due to the presence of nuclear forces.
Nuclear forces are weaker than the Coulomb force at separations of more than approximately 10^(-15) m, but stronger at separations of 10^(-15) m or less.

Quantization of Charge

Experimentally, the charge on an object is always an integral multiple of the charge of an electron (1.6 × 10^(-19) C), i.e., q = ne, where n = 1, 2, 3, ... .
This property of charge is called quantization of charge, with e being the smallest unit of charge and called the elementary charge.
Charge is additive, meaning the total charge on a body is the algebraic sum of the charges at different parts of the body.

Conservation of Charge

The total amount of charge in an isolated system is always constant.
Charge may be transferred within the system, but the net charge remains the same.
Charge cannot be created or destroyed, following the law of conservation of charge.
Examples supporting this law include the transfer of charge when rubbing a glass rod with silk.

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Description

Understand the fundamental principles of Coulomb's Law, including the types of electric charges, force relationships, and mathematical representation. Learn how to apply Coulomb's Law to real-world scenarios.