To determine the force between the two charges and whether it is attractive or repulsive, let's consider the following steps:
### Step 1: Understand Coulomb's Law
Coulomb's Law states that the magnitude of the electrostatic force [tex]\( F \)[/tex] between two point charges is directly proportional to the product of the absolute values of the charges and inversely proportional to the square of the distance between them. The formula is:
[tex]\[ F = k \frac{|q_1 q_2|}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the magnitude of the force between the two charges,
- [tex]\( k \)[/tex] is Coulomb's constant ([tex]\(8.99 \times 10^9 \; N \cdot m^2 / C^2 \)[/tex]),
- [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the amounts of the two charges,
- [tex]\( r \)[/tex] is the distance between the centers of the two charges.
### Step 2: Plug in the Given Values
Given:
- [tex]\( q_1 = +5 \, C \)[/tex],
- [tex]\( q_2 = -9 \, C \)[/tex],
- [tex]\( r = 1 \, m \)[/tex].
The magnitude of the force can be calculated as:
[tex]\[ F = k \frac{|q_1 q_2|}{r^2} \][/tex]
[tex]\[ F = 8.99 \times 10^9 \frac{|5 \times (-9)|}{1^2} \][/tex]
[tex]\[ F = 8.99 \times 10^9 \times 45 \][/tex]
[tex]\[ F = 404550000000 \, N \][/tex]
So, the magnitude of the force is [tex]\( 404550000000 \, N \)[/tex].
### Step 3: Determine the Force Direction
The charges are of opposite signs (one is positive and the other is negative). According to the principles of electrostatics, opposite charges attract each other. Therefore, the force will be attractive.
### Step 4: Represent the Force on a Diagram
Since we have determined that the force is attractive, the force vectors will be directed towards each other, indicating that the charges are pulling towards each other.
Here is what the diagram would look like:
```
+5 C <--- 404550000000 N ---> -9 C
```
In this diagram:
- The charge [tex]\( +5 \, C \)[/tex] experiences a force of [tex]\( 404550000000 \, N \)[/tex] towards the charge [tex]\( -9 \, C \)[/tex].
- Similarly, the charge [tex]\( -9 \, C \)[/tex] experiences a force of [tex]\( 404550000000 \, N \)[/tex] towards the charge [tex]\( +5 \, C \)[/tex].
Thus, the correct representation of the force between the two charges is an attractive force with a magnitude of [tex]\( 404550000000 \, N \)[/tex]. This diagram shows that both charges attract each other with the same magnitude of force.
