Question

For this part, we will be adjusting the size of CHARGE 1 ONLY.
Set the distance between the two charges for 4 cm
Set charge 2 for 8 µC
Given the charge values and the distances, determine the electrostatic force between the charged particles and if they are attracted, repelled, or neither. (**Remember, like charges repel and opposite charges attract)



Column A
Column A
1.
Trial 1: Force =:
Trial 1: Force =
2.
Trial 2: Force =:
Trial 2: Force =
3.
Trial 3: Force =:
Trial 3: Force =
4.
Trial 4: Force =:
Trial 4: Force =
5.
Trial 1: Are the two charge ions attracted, repelled, or neither?:
Trial 1: Are the two charge ions attracted, repelled, or neither?
6.
Trial 2: Are the two charge ions attracted, repelled, or neither?:
Trial 2: Are the two charge ions attracted, repelled, or neither?
7.
Trial 3: Are the two charge ions attracted, repelled, or neither?:
Trial 3: Are the two charge ions attracted, repelled, or neither?
8.
Trial 4: Are the two charge ions attracted, repelled, or neither?:
Trial 4: Are the two charge ions attracted, repelled, or neither?
Column B
Column B
a.79.889 N
b.179.751 N
c.Repelled
d.Neither
e.359.502 N
f.44.938 N
g.269.627 N
h.89.876 N
i.Attracted

Answer 1

To determine the electrostatic force between two charges, we can use Coulomb's Law, given by the formula:

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

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

### Given:
- Distance, \( r = 4 \, \text{cm} = 0.04 \, \text{m} \)
- Charge 2, \( q_2 = 8 \, \mu\text{C} = 8 \times 10^{-6} \, \text{C} \)

Now, to process the trials, we need a value for Charge 1 (\( q_1 \)). Let's assume \( q_1 \) takes on a few different values for the trials. Let's say:

- Trial 1: \( q_1 = 5 \, \mu\text{C} = 5 \times 10^{-6} \, \text{C} \)
- Trial 2: \( q_1 = 10 \, \mu\text{C} = 10 \times 10^{-6} \, \text{C} \)
- Trial 3: \( q_1 = -5 \, \mu\text{C} = -5 \times 10^{-6} \, \text{C} \)
- Trial 4: \( q_1 = -10 \, \mu\text{C} = -10 \times 10^{-6} \, \text{C} \)

Calculating the forces for each trial:

### Trial 1
- \( q_1 = 5 \times 10^{-6} \)
\[
F = 8.99 \times 10^9 \cdot \frac{(5 \times 10^{-6})(8 \times 10^{-6})}{(0.04)^2}
\]
\[
F = 8.99 \times 10^9 \cdot \frac{40 \times 10^{-12}}{0.0016}
\]
\[
F = 8.99 \times 10^9 \cdot 25 \times 10^{-6}
\]
\[
F = 224.75 \, \text{N} \quad (\text{Repelled, since both are positive})
\]

### Trial 2
- \( q_1 = 10 \times 10^{-6} \)
\[
F = 8.99 \times 10^9 \cdot \frac{(10 \times 10^{-6})(8 \times 10^{-6})}{(0.04)^2}
\]
\[
F = 8.99 \times 10^9 \cdot \frac{80 \times 10^{-12}}{0.0016}
\]
\[
F = 8.99 \times 10^9 \cdot 50 \times 10^{-6}
\]
\[
F = 449.5 \, \text{N} \quad (\text{Repelled})
\]

### Trial 3
- \( q_1 = -5 \times 10^{-6} \)
\[
F = 8.99 \times 10^9 \cdot \frac{(-5 \times 10^{-6})(8 \times 10^{-6})}{(0.04)^2}
\]
\[
F = 8.99 \times 10^9 \cdot \frac{-40 \times 10^{-12}}{0.0016}
\]
\[
F = -224.75 \, \text{N} \quad (\text{Attracted, since one is negative})
\]

### Trial 4
- \( q_1 = -10 \times 10^{-6} \)
\[
F = 8.99 \times 10^9 \cdot \frac{(-10 \times 10^{-6})(8 \times 10^{-6})}{(0.04)^2}
\]
\[
F = 8.99 \times 10^9 \cdot \frac{-80 \times 10^{-12}}{0.0016}
\]
\[
F = -449.5 \, \text{N} \quad (\text{Attracted})
\]

### Summary of Results:
- **Trial 1:** Force = 224.75 N, Repelled
- **Trial 2:** Force = 449.5 N, Repelled
- **Trial 3:** Force = 224.75 N, Attracted
- **Trial 4:** Force = 449.5 N, Attracted

### Filling in the Columns
Using the calculations:
- Trial 1: Force = 224.75 N, **Repelled**
- Trial 2: Force = 449.5 N, **Repelled**
- Trial 3: Force = 224.75 N, **Attracted**
- Trial 4: Force = 449.5 N, **Attracted**

Here’s how to fill the columns accordingly:

**Column A**
1. Trial 1: Force = 224.75 N
2. Trial 2: Force = 449.5 N
3. Trial 3: Force = 224.75 N
4. Trial 4: Force = 449.5 N
5. Trial 1: Are the two charge ions attracted, repelled, or neither?: Repelled
6. Trial 2: Are the two charge ions attracted, repelled, or neither?: Repelled
7. Trial 3: Are the two charge ions attracted, repelled, or neither?: Attracted
8. Trial 4: Are the two charge ions attracted, repelled, or neither?: Attracted

**Column B**
1. (corresponding force values and attraction/repulsion status)