Two charges, 5x10^-6C and 4x10^-6C experience a repulsive force of 80N. Find the distance between the charges

To solve this problem, we can use **Coulomb's Law**, which describes the electrostatic force between two point charges. The formula is:

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

Where:
- \( F \) is the electrostatic force (80 N),
- \( q_1 \) and \( q_2 \) are the charges (5 × 10⁻⁶ C and 4 × 10⁻⁶ C),
- \( r \) is the distance between the charges (which we need to find),
- \( k_e \) is Coulomb's constant, approximately \( 8.99 \times 10^9 \, \text{N·m}^2/\text{C}^2 \).

### Step-by-step calculation:

1. **Substitute the known values into the equation:**

\[
80 = \frac{(8.99 \times 10^9) \times |(5 \times 10^{-6}) \times (4 \times 10^{-6})|}{r^2}
\]

2. **Calculate the numerator:**

\[
(5 \times 10^{-6}) \times (4 \times 10^{-6}) = 20 \times 10^{-12} \, \text{C}^2
\]

So the equation becomes:

\[
80 = \frac{8.99 \times 10^9 \times 20 \times 10^{-12}}{r^2}
\]

3. **Simplify the equation:**

\[
80 = \frac{179.8 \times 10^{-3}}{r^2}
\]

4. **Solve for \( r^2 \):**

\[
r^2 = \frac{179.8 \times 10^{-3}}{80}
\]

\[
r^2 = 2.2475 \times 10^{-3}
\]

5. **Take the square root to find \( r \):**

\[
r = \sqrt{2.2475 \times 10^{-3}} \approx 0.0474 \, \text{m}
\]

### Final Answer:
The distance between the charges is approximately **0.0474 meters**, or **4.74 cm**.

Would you like more details on this problem, or do you have any questions? Here are some related questions:

1. What is the effect of increasing one of the charges on the electrostatic force?
2. How does the force change if the distance between the charges is doubled?
3. What happens to the force if both charges are negative instead of positive?
4. How can we measure the electrostatic force experimentally?
5. How does Coulomb’s Law relate to electric fields?

**Tip:** When working with Coulomb's law, always check the signs of the charges to determine if the force is attractive (opposite charges) or repulsive (like charges).

Two charges, 5x10^-6C and 4x10^-6C experience a repulsive force of 80N. Find the distance between the charges.

Learn how to calculate the distance between two charges given the electrostatic force using Coulomb's Law. In this problem, two charges of 5x10^-6C and 4x10^-6C experience a repulsive force of 80N. A step-by-step solution shows how to find the distance between the charges.

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