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Chapter 3: Problem 56

Explain Coulomb's law.

Short Answer

Expert verified
Coulomb's law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It's represented by the formula \( F = k \frac{|q_{1} q_{2}|}{r^{2}} \). Four parameters are involved, \( q_{1} \) and \( q_{2} \) (the magnitudes of the charges), \( r \) (the distance between the charges), and \( k \) (Coulomb's constant).

Step by step solution

01

Statement of Coulomb's Law

Coulomb's law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of their distance apart. It can be expressed mathematically as \( F = k \frac{|q_{1} q_{2}|}{r^{2}} \) where \( F \) is the magnitude of the force between the charges, \( q_{1} \) and \( q_{2} \) are the amounts of charge, \( r \) is the distance separating the charges and \( k \) is Coulomb's constant.
02

Parameters Involved

There are four parameters involved in Coulomb's law. The first two are \( q_{1} \) and \( q_{2} \), which represent the magnitudes of the two charges. \( r \) represents the distance between the centres of the two charges. It is important to specify that it is the distance between the centres of the charges, and not the distance from edge to edge. The last parameter, \( k \), is Coulomb's constant. It is a proportionality constant that appears in Coulomb's law. Its value in SI units is approximately \( 8.99 \times 10^{9} \) N(m^2/C^2).
03

Calculation using Coulomb's law

To calculate the force between two charges using Coulomb's law, we identify the charges and the distance between them. Then insert these values into the formula in place of \( q_{1} \), \( q_{2} \), and \( r \). Use the value of \( k \) as \( 8.99 \times 10^{9} \) N(m^2/C^2). After doing this, carry out the necessary multiplication and division to find the force \( F \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electrostatics
Electrostatics refers to the study of forces, fields, and potentials arising from static electric charges. Imagine tiny beads or balloons that carry electric charges remaining perfectly still. That is what we consider in electrostatics, where the charges are not moving.
Electrostatics helps us understand how charged particles interact when at rest, which can eventually predict how electric forces come into play.
  • Static Charges: Only charges that aren't moving are considered. They exert force on each other, even though they remain in place.
  • Electric Fields: An electric field is formed around any charged particle. This invisible field explains the charge's ability to exert force on another charge without coming into direct contact.
  • Electric Potential: It is the amount of work needed to move a charge within an electric field. It is usually measured in volts and linked to the concept of voltage.
Electrostatics is foundational in physics for exploring how objects are attracted or repelled, which leads to the calculation of forces such as those explained by Coulomb鈥檚 Law.
Electric Force
The electric force is a fundamental interaction between charged particles. Picture it as a push or pull effect stemming from the electric charge. This is what we observe when balloons stick to each other or when your hair stands after removing a sweater. Coulomb's law is instrumental in describing this electric force quantitatively.
  • Magnitude and Direction: The electric force is a vector quantity, meaning it has both magnitude (how strong) and direction (which way).
  • Attraction and Repulsion: Like charges repel each other, while opposite charges attract. Therefore, two electrons will push away from each other, but an electron and a proton will come together.
  • Dependence on Charges and Distance: As Coulomb's Law shows, the force increases with the charges' magnitude and decreases with increased distance. Two small charges far apart exert a weaker force compared to large charges up close.
Understanding electric force allows us to predict how charged particles will interact in an electrostatic setup. This is integral in fields such as chemistry, electronics, and material science.
Charges Interaction
Charges interaction is the fundamental basis of electrostatic reactions. The interaction occurs due to the forces the charged objects emit. We can understand it further with the help of Coulomb's Law.
  • Mutual Influence: Each charge affects the other, resulting in a force exerted on both, illustrating Newton's third law. If Charge1 repels Charge2, Charge2 will repel Charge1 equally and oppositely.
  • Fields and Interaction: Each charge has its electric field influencing neighboring charges. The interaction seen is the culmination of these electric fields overlapping.
  • Practical Effects: Everyday occurrences like static electricity, lightning, or even the behavior of particles in dust clouds in space stem from charges interacting with each other.
Charges interaction not only dictates the small-scale behaviors of particles but also influences vast natural phenomena. Understanding these interactions helps us grasp the underlying principles governing matter and energies in the universe.

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