Given two charges q1=5 μC and q2=−5 μC are separated by a distance r in a vacuum. If the magnitude of the force between them is 1 N, what is the separation distance r?
a) 1.5 m
b) 0.1 m
c) 0.3 m
d) 0.5 m

To find the separation distance \( r \) between the charges \( q_1 \) and \( q_2 \), we can use Coulomb's Law, which states that the force \( F \) between two charges is given by:

\[ F = k \frac{|q_1 q_2|}{r^2} \]

where:
- \( F \) is the magnitude of the force between the charges,
- \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the separation distance between the charges.

Given:
- \( F = 1 \, \text{N} \),
- \( q_1 = 5 \, \mu\text{C} = 5 \times 10^{-6} \, \text{C} \),
- \( q_2 = -5 \, \mu\text{C} = -5 \times 10^{-6} \, \text{C} \).

Let's solve for \( r \):

\[ 1 = 8.99 \times 10^9 \cdot \frac{(5 \times 10^{-6}) \cdot (5 \times 10^{-6})}{r^2} \]

First, simplify the numerator:

\[ (5 \times 10^{-6}) \cdot (5 \times 10^{-6}) = 25 \times 10^{-12} \, \text{C}^2 \]

Now substitute back into the equation:

\[ 1 = 8.99 \times 10^9 \cdot \frac{25 \times 10^{-12}}{r^2} \]

\[ 1 = \frac{8.99 \times 10^9 \cdot 25 \times 10^{-12}}{r^2} \]

\[ 1 = \frac{224.75 \times 10^{-3}}{r^2} \]

\[ 1 = \frac{0.22475}{r^2} \]

Now, solve for \( r^2 \):

\[ r^2 = 0.22475 \]

\[ r = \sqrt{0.22475} \]

\[ r \approx 0.474 \, \text{m} \]

Comparing this to the given options:

a) 1.5 m  
b) 0.1 m  
c) 0.3 m  
d) 0.5 m  

The closest answer is \( d) 0.5 \, \text{m} \).

Thus, the separation distance \( r \) is approximately \( 0.5 \, \text{m} \).

Would you like more details or have any questions?

Here are five more questions you might want to ask:
1. How do you derive Coulomb's Law?
2. What are the units of Coulomb's constant \( k \)?
3. Can you explain how to convert microcoulombs to coulombs?
4. What are some applications of Coulomb's Law in real life?
5. How does the force between charges change if one of the charges is doubled?

**Tip:** Always ensure that the units are consistent when using formulas in physics to avoid calculation errors.

Learn how to calculate the separation distance between charges q1 = 5 µC and q2 = -5 µC using Coulomb's Law. Given the force between them is 1 N, find the distance in meters. Suitable for advanced high school physics students.

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