What is the repulsive force between two pith balls that are 8.00 cm apart and have equal charges of – 30.0 nC?

To find the repulsive force between the two pith balls, we can use Coulomb's Law. Coulomb's Law states:

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

Where:
- \( F \) is the magnitude of the force between the charges,
- \( k_e \) is Coulomb's constant, approximately \( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \),
- \( q_1 \) and \( q_2 \) are the charges (in Coulombs),
- \( r \) is the distance between the charges (in meters).

Given:
- \( q_1 = q_2 = -30.0 \, \text{nC} = -30.0 \times 10^{-9} \, \text{C} \),
- \( r = 8.00 \, \text{cm} = 0.0800 \, \text{m} \).

Let's calculate the force.

\[
F = \left( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \right) \cdot \frac{(30.0 \times 10^{-9} \, \text{C})^2}{(0.0800 \, \text{m})^2}
\]

Now let's compute it:

\[
F = \left( 8.99 \times 10^9 \right) \cdot \frac{(900 \times 10^{-18})}{0.0064} \, \text{N}
\]

\[
F = \left( 8.99 \times 10^9 \right) \cdot \left( 1.40625 \times 10^{-13} \right) \, \text{N}
\]

\[
F \approx 1.26 \times 10^{-3} \, \text{N}
\]

So, the repulsive force between the two pith balls is approximately \( 1.26 \, \text{mN} \) (milliNewtons).

Would you like any further details or have any other questions?

---

**Relative Questions:**
1. How would the force change if the distance between the pith balls were doubled?
2. What would happen to the force if the charges on the pith balls were increased to \( 60.0 \, \text{nC} \)?
3. What is the significance of the negative sign in the charge, and how does it affect the force?
4. How would the force change if the charges were of opposite signs?
5. What are some real-world applications of Coulomb's Law?

**Tip:** Always make sure to convert units to the SI system (meters, coulombs, etc.) when using Coulomb's Law for accurate calculations.

Learn how to calculate the repulsive force between two pith balls that are 8.00 cm apart and have equal charges of -30.0 nC using Coulomb's Law. Understand the impact of charge and distance on electrostatic forces. Suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation