To determine the electrostatic force between two charged particles using Coulomb’s Law, we can use the formula:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
Where:
- \( F \) is the electrostatic force,
- \( k \) is Coulomb's constant (\( 8.99 \times 10^9 , \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges (in coulombs),
- \( r \) is the distance between the charges (in meters).
In your problem:
- Distance \( r = 4 , \text{cm} = 0.04 , \text{m} \)
- \( q_2 = 8 , \mu\text{C} = 8 \times 10^{-6} , \text{C} \)
Let’s denote the charge of Charge 1 as \( q_1 \) and consider it in different trial values.
Since you've mentioned varying \( q_1 \) and provided force options, let’s break down what values might fit into different scenarios of \( q_1 \) along with the respective conclusions about attraction or repulsion.
Here’s how you can fill in the trials based on your provided options:
-
Force Calculation for Different Charges:
- Trial 1: Assume \( q_1 \) = 1 µC = \( 1 \times 10^{-6} , \text{C} \) \[ F = k \frac{|q_1 \cdot q_2|}{r^2} = (8.99 \times 10^9) \cdot \frac{|1 \times 10^{-6} \cdot 8 \times 10^{-6}|}{(0.04)^2} = 89.876 , \text{N} \]
- Trial 2: Assume \( q_1 \) = 2 µC = \( 2 \times 10^{-6} , \text{C} \) \[ F = (8.99 \times 10^9) \cdot \frac{|2 \times 10^{-6} \cdot 8 \times 10^{-6}|}{(0.04)^2} = 179.751 , \text{N} \]
- Trial 3: Assume \( q_1 \) = 3 µC = \( 3 \times 10^{-6} , \text{C} \) \[ F = (8.99 \times 10^9) \cdot \frac{|3 \times 10^{-6} \cdot 8 \times 10^{-6}|}{(0.04)^2} = 269.627 , \text{N} \]
- Trial 4: Assume \( q_1 \) = 4 µC = \( 4 \times 10^{-6} , \text{C} \) \[ F = (8.99 \times 10^9) \cdot \frac{|4 \times 10^{-6} \cdot 8 \times 10^{-6}|}{(0.04)^2} = 359.502 , \text{N} \]
-
Determine Attraction or Repulsion:
- For all trials, if both charges are of the same sign (positive-positive or negative-negative), they will repel each other. If they are of opposite signs, they will attract. Since charge \( q_2 \) is positive (8 µC), the answer will depend on the sign of \( q_1 \).
Assuming \( q_1 \) is of the same sign (positive):
- Trial 1: Repelled
- Trial 2: Repelled
- Trial 3: Repelled
- Trial 4: Repelled
Based on the calculations and assumptions stated, here's how to fill in your table:
Column A
- Trial 1: Force = 89.876 N
- Trial 2: Force = 179.751 N
- Trial 3: Force = 269.627 N
- Trial 4: Force = 359.502 N
- Trial 1: Are the two charge ions attracted, repelled, or neither?: Repelled
- Trial 2: Are the two charge ions attracted, repelled, or neither?: Repelled
- Trial 3: Are the two charge ions attracted, repelled, or neither?: Repelled
- Trial 4: Are the two charge ions attracted, repelled, or neither?: Repelled
You can replace the charge values (trial conditions) accordingly as per your simulation or experimental design if the assumptions about charge sign differ.
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