Coulomb's Law: Understanding Its Real-World Applications

Coulomb's law, a principle formulated by 18th-century French physicist Charles-Augustin de Coulomb, describes the electric force between charged objects. The law is analogous to Newton's law of gravity, with both forces decreasing as the square of the distance between objects increases. Coulomb's law is used to determine the force between two point charges and can be applied to situations with more than two charges. In such cases, the system can be represented as a superposition of individual point charges, and the forces can be combined to determine the net force acting on each charge. However, Coulomb's law is only valid for point charges with static positions, as moving charges introduce additional magnetic effects that influence the force between charges.

Attraction and repulsion of two charged bodies

Coulomb's law, a mathematical description of the electric force between charged objects, was formulated by 18th-century French physicist Charles-Augustin de Coulomb. It is analogous to Isaac Newton's law of gravity, with both laws featuring an inverse-square relationship between the force and the distance between the objects. However, the magnitude and sign of the electric force in Coulomb's law are determined by the electric charge of an object, while Newton's law of gravity depends on the mass of the object.

Coulomb's law states that like charges repel each other, while unlike charges attract. This means that two negatively charged objects will repel each other, whereas a positively charged object will attract a negatively charged one. The attraction or repulsion acts along the line between the two charges.

The size of the force described by Coulomb's law varies inversely with the square of the distance between the charges. If the distance between the charges is doubled, the force of attraction or repulsion becomes four times weaker. Conversely, if the charges are brought ten times closer, the force becomes 100 times stronger.

The magnitude of the force is also directly proportional to the value of each charge. For example, consider two positive charges, one of 0.1 coulombs and the other of 0.2 coulombs. They would repel each other with a force that depends on the product of their charges (0.2 x 0.1). If both charges were halved, the repulsion would be reduced to a quarter of its original strength.

Coulomb's law can be used to describe the attraction and repulsion between any charged particles, including atomic particles. In a multi-electron atom, electrons are negatively charged and are attracted to the positive charge of the nucleus. However, these electrons also repel each other. Coulomb's law can describe the attractive force between a nucleus and an electron, as well as the repulsive force between two electrons.

Electrostatic force

Coulomb's law, or Coulomb's inverse-square law, describes the electrostatic force, or the force between two electrically charged particles at rest. The law was formulated by 18th-century French physicist Charles-Augustin de Coulomb and is analogous to Isaac Newton's law of gravity.

The electrostatic force is the force of attraction or repulsion between two charged particles. It is also called Coulomb's force or Coulomb's interaction. For example, the force between the protons and electrons in an atom is electrostatic and is responsible for the atom's stability.

Coulomb's law states that the magnitude or absolute value of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them.

In simpler terms, the law can be summarised as:

• Like charges repel each other; unlike charges attract.
• The attraction or repulsion acts along the line between the two charges.
• The size of the force varies inversely with the square of the distance between the two charges. Therefore, if the distance between the charges is doubled, the attraction or repulsion becomes weaker, decreasing to a quarter of its original value. If the charges come ten times closer, the force increases by a factor of 100.
• The size of the force is proportional to the value of each charge.

The unit used to measure charge is the coulomb (C). The electrostatic force unit is N (Newton).

Coulomb's law can be applied to situations with more than two point charges. The law of superposition allows the law to be extended to include any number of point charges. The force acting on a point charge due to a system of point charges is the vector addition of the individual forces acting alone on that point charge due to each of the charges.

Coulomb's law is essential to the development of the theory of electromagnetism and is used in laser and inkjet printers, Van de Graaff generators, and smoke precipitators.

Inverse square law

Coulomb's Law, or the inverse-square law, is a fundamental principle in physics that describes the electric force between charged objects. Formulated by French physicist Charles-Augustin de Coulomb in the 18th century, it is similar in structure to Isaac Newton's law of universal gravitation.

Coulomb's Law states that the magnitude of the attractive or repulsive electrostatic force between two electrically charged particles at rest is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them. In simpler terms, the law explains that as the distance between two charged objects increases, the force between them decreases, and vice versa. This relationship follows the inverse square law, which is also observed in gravity, magnetism, and light intensity.

The law can be mathematically expressed as:

> {\displaystyle |F|=k_{\text{e}}{\frac {|q_{1}||q_{2}|}{r^{2}}}}

Where ke is a constant, q1 and q2 represent the magnitudes of the charges, and r is the distance between them.

Coulomb's Law has broad applications and is essential for understanding the behaviour of charged particles. It can be used to explain the force between two point charges, such as in the example of three fixed point charges on a straight line. It also plays a crucial role in the development of electromagnetism and the understanding of atomic and molecular interactions.

Permittivity of free space

Coulomb's law describes the electric force between charged objects. It was formulated by 18th-century French physicist Charles-Augustin de Coulomb and is analogous to Isaac Newton's law of gravity.

The permittivity of free space measures the ability of a vacuum to support an electric field. It is a measure of opposition, where higher permittivity results in a lower electric field from a given source of electric field (a charge).

The permittivity of a vacuum is approximately 8.854 x 10^-12 square coulombs per newton square metre (C²·kg⁻¹·m⁻³·s² in SI units). It is used to relate the units for electric charge to mechanical quantities such as length and force. For example, Coulomb's law can be used to calculate the force between two separated electric charges with spherical symmetry in a vacuum:

> F_C = (1 / 4π ε0) * (q1 * q2 / r^2)

Here, q1 and q2 are the charges, r is the distance between their centres, and the value of the constant fraction 1/(4π ε0) is approximately 9 x 10^9 N·m²·C⁻².

The permittivity of free space also appears in Maxwell's equations, which describe the properties of electric and magnetic fields, electromagnetic radiation, and their sources. In electrical engineering, ε0 is used to quantify the permittivity of various dielectric materials.

The value of ε0 is defined by the formula:

> ε0 = 1 / (μ0 * c^2)

Where c is the speed of light in a classical vacuum in SI units, and μ0 is the magnetic constant, or permeability of free space.

The permittivity of free space is a fundamental constant that characterises the behaviour of electric fields in a vacuum, prior to the introduction of a medium that can influence the field. It is a property of space itself and is related to the measurement system used.

Electric field

Coulomb's law is a fundamental principle in physics that describes the electric force between charged objects. It was formulated by the 18th-century French physicist Charles-Augustin de Coulomb and is analogous to Isaac Newton's law of gravity. The law states that the magnitude of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of their charge magnitudes and inversely proportional to the square of the distance between them.

Now, let's discuss how this relates to the electric field:

An electric field is a vector field that can be used to calculate the force experienced by a positive test charge placed at a specific point in space due to the influence of other charges. The electric field is a more versatile concept than simply considering the force between two charges because it allows us to understand how a single charge affects the space around it.

The electric field is defined as the ratio of the Coulomb force to the test charge. Mathematically, this is represented as E = F/q, where E is the electric field, F is the electrostatic force (Coulomb force), and q is the test charge. By defining the electric field in this way, we can determine how a specific arrangement of charges influences the space around it.

The electric field created by a point charge is not constant throughout space; its magnitude and direction vary with position. The magnitude of the electric field created by a point charge is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance from the charge. This means that as you move farther away from the charge, the electric field it creates will weaken. Additionally, the direction of the electric field lines depends on the sign of the charge. For a positive point charge, the electric field lines point radially outward, indicating that a positive test charge placed in that field would move away from the source charge. On the other hand, for a negative point charge, the electric field lines point radially inward, indicating that a positive test charge would be attracted toward the source charge.

The electric field concept is particularly useful when dealing with more complex charge distributions, such as continuous charge distributions. In such cases, the principle of superposition is used, where the total electric field at a point is the vector sum of the fields created by each individual charge. This allows us to calculate and predict the behaviour of charges within electric fields, making it a fundamental concept in understanding electrostatics.

Frequently asked questions