Sure! Let's proceed step-by-step to calculate the force between \( q_1 \) and \( q_2 \) using Coulomb's Law.
### Step 1: Understanding Coulomb's Law
Coulomb's Law gives us the magnitude of the force between two point charges. The formula is:
[tex]\[
\vec{F}_2 = k_e \frac{\left|q_1 q_2\right|}{r^2}
\][/tex]
where:
- \( \vec{F}_2 \) is the force between the charges.
- \( k_e \) is Coulomb's constant, which is \( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \).
- \( q_1 \) and \( q_2 \) are the values of the two charges.
- \( r \) is the distance between the centers of the two charges.
### Step 2: Given Values
From the problem, we have:
- \( k_e = 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)
- \( r = 0.25 \, \text{m} \)
- Charges \( q_1 \) and \( q_2 \) are both assumed to be \( 1 \, \text{C} \).
### Step 3: Applying Values to the Formula
Substitute the given values into Coulomb's Law:
[tex]\[
\vec{F}_2 = k_e \frac{\left|q_1 q_2\right|}{r^2}
\][/tex]
### Step 4: Calculation
Substitute the known values:
[tex]\[
\vec{F}_2 = 8.99 \times 10^9 \frac{\left|1 \times 1\right|}{(0.25)^2}
\][/tex]
Simplify the denominator:
[tex]\[
(0.25)^2 = 0.0625
\][/tex]
Now, substitute:
[tex]\[
\vec{F}_2 = 8.99 \times 10^9 \frac{1}{0.0625}
\][/tex]
Calculate the fraction:
[tex]\[
\frac{1}{0.0625} = 16
\][/tex]
So, substituting back:
[tex]\[
\vec{F}_2 = 8.99 \times 10^9 \times 16
\][/tex]
### Step 5: Final Calculation
Multiply the numbers:
[tex]\[
\vec{F}_2 = 143.84 \times 10^9 \, \text{N}
\][/tex]
Thus, the force between the charges is:
[tex]\[
\vec{F}_2 = 143840000000.0 \, \text{N}
\][/tex]
Therefore, the magnitude of the force is [tex]\( \boxed{143840000000.0 \, \text{N}} \)[/tex].
