Join the IDNLearn.com community and start exploring a world of knowledge today. Our experts provide accurate and detailed responses to help you navigate any topic or issue with confidence.
Sagot :
To determine which pair of charges result in the largest repulsive force, we'll utilize the Coulomb's Law equation:
[tex]\[ F = \frac{k \cdot q_1 \cdot q_2}{R^2} \][/tex]
Where:
- [tex]\( F \)[/tex] is the force between two charges,
- [tex]\( k \)[/tex] is Coulomb's constant,
- [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the magnitudes of the two charges,
- [tex]\( R \)[/tex] is the distance between the charges.
Given pairs of charges are:
1. [tex]\(-3q\)[/tex] and [tex]\(-2q\)[/tex]
2. [tex]\(+3q\)[/tex] and [tex]\(-2q\)[/tex]
3. [tex]\(-2q\)[/tex] and [tex]\(+4q\)[/tex]
We should calculate the force for each given pair to determine which one has the largest repulsive force.
### Step-by-step Calculation:
#### Pair 1: [tex]\(-3q\)[/tex] and [tex]\(-2q\)[/tex]
[tex]\[ F_1 = \frac{k \cdot (-3q) \cdot (-2q)}{R^2} = \frac{k \cdot 6q^2}{R^2} \][/tex]
Since both charges are negative, the product [tex]\((-3q) \cdot (-2q)\)[/tex] is positive, leading to a repulsive force.
#### Pair 2: [tex]\(+3q\)[/tex] and [tex]\(-2q\)[/tex]
[tex]\[ F_2 = \frac{k \cdot (+3q) \cdot (-2q)}{R^2} = \frac{k \cdot (-6q^2)}{R^2} \][/tex]
The product [tex]\((+3q) \cdot (-2q)\)[/tex] is negative, leading to an attractive force, not repulsive.
#### Pair 3: [tex]\(-2q\)[/tex] and [tex]\(+4q\)[/tex]
[tex]\[ F_3 = \frac{k \cdot (-2q) \cdot (+4q)}{R^2} = \frac{k \cdot (-8q^2)}{R^2} \][/tex]
The product [tex]\((-2q) \cdot (+4q)\)[/tex] is negative, leading to an attractive force, not repulsive.
### Comparing Repulsive Forces:
Only Pair 1 results in a repulsive force. Therefore, the force corresponding to Pair 1 is:
[tex]\[ F_1 = \frac{6kq^2}{R^2} \][/tex]
After following through with the calculations, we see that the:
- Force for Pair 1 is [tex]\( 6.0 \)[/tex] units (repulsive force),
- Forces for Pair 2 and Pair 3 are -6.0 and -8.0 units (attractive forces).
Therefore, the largest repulsive force is produced by the pair of charges:
[tex]\(\boxed{-3q \text{ and } -2q}\)[/tex]
[tex]\[ F = \frac{k \cdot q_1 \cdot q_2}{R^2} \][/tex]
Where:
- [tex]\( F \)[/tex] is the force between two charges,
- [tex]\( k \)[/tex] is Coulomb's constant,
- [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the magnitudes of the two charges,
- [tex]\( R \)[/tex] is the distance between the charges.
Given pairs of charges are:
1. [tex]\(-3q\)[/tex] and [tex]\(-2q\)[/tex]
2. [tex]\(+3q\)[/tex] and [tex]\(-2q\)[/tex]
3. [tex]\(-2q\)[/tex] and [tex]\(+4q\)[/tex]
We should calculate the force for each given pair to determine which one has the largest repulsive force.
### Step-by-step Calculation:
#### Pair 1: [tex]\(-3q\)[/tex] and [tex]\(-2q\)[/tex]
[tex]\[ F_1 = \frac{k \cdot (-3q) \cdot (-2q)}{R^2} = \frac{k \cdot 6q^2}{R^2} \][/tex]
Since both charges are negative, the product [tex]\((-3q) \cdot (-2q)\)[/tex] is positive, leading to a repulsive force.
#### Pair 2: [tex]\(+3q\)[/tex] and [tex]\(-2q\)[/tex]
[tex]\[ F_2 = \frac{k \cdot (+3q) \cdot (-2q)}{R^2} = \frac{k \cdot (-6q^2)}{R^2} \][/tex]
The product [tex]\((+3q) \cdot (-2q)\)[/tex] is negative, leading to an attractive force, not repulsive.
#### Pair 3: [tex]\(-2q\)[/tex] and [tex]\(+4q\)[/tex]
[tex]\[ F_3 = \frac{k \cdot (-2q) \cdot (+4q)}{R^2} = \frac{k \cdot (-8q^2)}{R^2} \][/tex]
The product [tex]\((-2q) \cdot (+4q)\)[/tex] is negative, leading to an attractive force, not repulsive.
### Comparing Repulsive Forces:
Only Pair 1 results in a repulsive force. Therefore, the force corresponding to Pair 1 is:
[tex]\[ F_1 = \frac{6kq^2}{R^2} \][/tex]
After following through with the calculations, we see that the:
- Force for Pair 1 is [tex]\( 6.0 \)[/tex] units (repulsive force),
- Forces for Pair 2 and Pair 3 are -6.0 and -8.0 units (attractive forces).
Therefore, the largest repulsive force is produced by the pair of charges:
[tex]\(\boxed{-3q \text{ and } -2q}\)[/tex]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.
