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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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