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Sagot :
### Solution:
Let's break down the problem step-by-step and find the force between the two charged particles and the direction in which particle [tex]\( q_2 \)[/tex] will want to move.
Given Information:
- Charge [tex]\( q_1 = 6 \, \mu C = 6 \times 10^{-6} \, C \)[/tex]
- Charge [tex]\( q_2 = 2 \, \mu C = 2 \times 10^{-6} \, C \)[/tex]
- Distance between the charges [tex]\( d = 0.1 \, m \)[/tex]
- Coulomb's constant [tex]\( k = 8.99 \times 10^9 \, N \cdot \frac{m^2}{C^2} \)[/tex]
#### Step-by-Step Calculation:
1. Coulomb’s Law Formula:
The force [tex]\( F \)[/tex] between two charges is given by Coulomb's law:
[tex]\[ F = k \cdot \frac{|q_1 \cdot q_2|}{d^2} \][/tex]
2. Substitute the given values:
- [tex]\( q_1 = 6 \times 10^{-6} \, C \)[/tex]
- [tex]\( q_2 = 2 \times 10^{-6} \, C \)[/tex]
- [tex]\( d = 0.1 \, m \)[/tex]
- [tex]\( k = 8.99 \times 10^9 \, N \cdot \frac{m^2}{C^2} \)[/tex]
[tex]\[ F = 8.99 \times 10^9 \cdot \frac{(6 \times 10^{-6}) \cdot (2 \times 10^{-6})}{(0.1)^2} \][/tex]
3. Calculate the numerator:
[tex]\[ (6 \times 10^{-6}) \cdot (2 \times 10^{-6}) = 12 \times 10^{-12} = 1.2 \times 10^{-11} \, C^2 \][/tex]
4. Calculate the denominator:
[tex]\[ (0.1)^2 = 0.01 \, m^2 \][/tex]
5. Compute the force:
[tex]\[ F = 8.99 \times 10^9 \cdot \frac{1.2 \times 10^{-11}}{0.01} \][/tex]
6. Simplify further:
[tex]\[ F = 8.99 \times 10^9 \cdot 1.2 \times 10^{-9} \][/tex]
[tex]\[ F = 10.788 \, N \][/tex]
Result:
The magnitude of the force between the two particles is approximately [tex]\( 10.788 \, N \)[/tex].
### Direction of Force:
Both charges [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are positive. According to Coulomb's law, like charges repel each other.
Therefore:
- Particle [tex]\( q_2 \)[/tex] will want to move away from particle [tex]\( q_1 \)[/tex].
Summary:
- Force Applied between [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex]: [tex]\( 10.788 \, N \)[/tex]
- Direction in which particle [tex]\( q_2 \)[/tex] wants to move: Away from [tex]\( q_1 \)[/tex], because the force is repulsive.
Let's break down the problem step-by-step and find the force between the two charged particles and the direction in which particle [tex]\( q_2 \)[/tex] will want to move.
Given Information:
- Charge [tex]\( q_1 = 6 \, \mu C = 6 \times 10^{-6} \, C \)[/tex]
- Charge [tex]\( q_2 = 2 \, \mu C = 2 \times 10^{-6} \, C \)[/tex]
- Distance between the charges [tex]\( d = 0.1 \, m \)[/tex]
- Coulomb's constant [tex]\( k = 8.99 \times 10^9 \, N \cdot \frac{m^2}{C^2} \)[/tex]
#### Step-by-Step Calculation:
1. Coulomb’s Law Formula:
The force [tex]\( F \)[/tex] between two charges is given by Coulomb's law:
[tex]\[ F = k \cdot \frac{|q_1 \cdot q_2|}{d^2} \][/tex]
2. Substitute the given values:
- [tex]\( q_1 = 6 \times 10^{-6} \, C \)[/tex]
- [tex]\( q_2 = 2 \times 10^{-6} \, C \)[/tex]
- [tex]\( d = 0.1 \, m \)[/tex]
- [tex]\( k = 8.99 \times 10^9 \, N \cdot \frac{m^2}{C^2} \)[/tex]
[tex]\[ F = 8.99 \times 10^9 \cdot \frac{(6 \times 10^{-6}) \cdot (2 \times 10^{-6})}{(0.1)^2} \][/tex]
3. Calculate the numerator:
[tex]\[ (6 \times 10^{-6}) \cdot (2 \times 10^{-6}) = 12 \times 10^{-12} = 1.2 \times 10^{-11} \, C^2 \][/tex]
4. Calculate the denominator:
[tex]\[ (0.1)^2 = 0.01 \, m^2 \][/tex]
5. Compute the force:
[tex]\[ F = 8.99 \times 10^9 \cdot \frac{1.2 \times 10^{-11}}{0.01} \][/tex]
6. Simplify further:
[tex]\[ F = 8.99 \times 10^9 \cdot 1.2 \times 10^{-9} \][/tex]
[tex]\[ F = 10.788 \, N \][/tex]
Result:
The magnitude of the force between the two particles is approximately [tex]\( 10.788 \, N \)[/tex].
### Direction of Force:
Both charges [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are positive. According to Coulomb's law, like charges repel each other.
Therefore:
- Particle [tex]\( q_2 \)[/tex] will want to move away from particle [tex]\( q_1 \)[/tex].
Summary:
- Force Applied between [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex]: [tex]\( 10.788 \, N \)[/tex]
- Direction in which particle [tex]\( q_2 \)[/tex] wants to move: Away from [tex]\( q_1 \)[/tex], because the force is repulsive.
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