Alright, let's explore how to determine the correct equation for calculating the electrical force, [tex]\( F_e \)[/tex], between two charges.
The concept we're examining is famously known as Coulomb's Law, which states that the electrical force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.
Here are the given options to consider:
1. [tex]\( F_e = k \frac{q_1 q_2}{d} \)[/tex]
2. [tex]\( F_e = \frac{q_1 q_2}{d^2} \)[/tex]
3. [tex]\( F = k \frac{q_1 q_2}{d^2} \)[/tex]
4. [tex]\( F_e = k \left( \frac{q_1 q_2}{d} \right)^2 \)[/tex]
Let's analyze each option:
1. [tex]\( F_e = k \frac{q_1 q_2}{d} \)[/tex]:
This expression does not match the standard form of Coulomb's Law, as it suggests that the force decreases linearly with distance, not with the square of the distance.
2. [tex]\( F_e = \frac{q_1 q_2}{d^2} \)[/tex]:
This equation correctly shows an inverse square relationship between the force and the distance. However, it is missing the constant of proportionality [tex]\( k \)[/tex].
3. [tex]\( F = k \frac{q_1 q_2}{d^2} \)[/tex]:
This equation accurately represents Coulomb's Law. It includes both the inverse square relationship and the constant [tex]\( k \)[/tex], which is Coulomb's constant.
4. [tex]\( F_e = k \left( \frac{q_1 q_2}{d} \right)^2 \)[/tex]:
This form is incorrect as it implies squaring the entire fraction [tex]\(\frac{q_1 q_2}{d}\)[/tex], which is not how Coulomb's Law is expressed.
Given the options, the correct equation that represents Coulomb's Law is:
[tex]\[ F = k \frac{q_1 q_2}{d^2} \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{3} \][/tex]
This formula indicates the electrical force [tex]\( F \)[/tex] between two charges [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] separated by a distance [tex]\( d \)[/tex], with [tex]\( k \)[/tex] being Coulomb's constant.
