To find the numerical values of the electrostatic force between two charges using Coulomb’s Law, we can express it with the formula:
\[ F = k \frac{|q_1 \times q_2|}{r^2} \]
where:
- \( F \) is the force between the charges,
- \( k \) 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,
- \( r \) is the distance between the charges.
For your case, \( q_2 = 8 , \mu C = 8 \times 10^{-6} , C \) and the distance \( r = 0.04 , m \) (4 cm). You would adjust \( q_1 \) for Trials 1-4.
Let's fill in the results based on the provided information, assuming the following values for \( q_1 \) for the trials:
- Trial 1: \( q_1 = 10 , \mu C = 10 \times 10^{-6} , C \)
- Trial 2: \( q_1 = 5 , \mu C = 5 \times 10^{-6} , C \)
- Trial 3: \( q_1 = 1 , \mu C = 1 \times 10^{-6} , C \)
- Trial 4: \( q_1 = 20 , \mu C = 20 \times 10^{-6} , C \)
Calculate the forces:
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For Trial 1: \[ F_1 = k \frac{|10 \times 10^{-6} \times 8 \times 10^{-6}|}{(0.04)^2} \approx 89.876 , N \]
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For Trial 2: \[ F_2 = k \frac{|5 \times 10^{-6} \times 8 \times 10^{-6}|}{(0.04)^2} \approx 44.938 , N \]
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For Trial 3: \[ F_3 = k \frac{|1 \times 10^{-6} \times 8 \times 10^{-6}|}{(0.04)^2} \approx 8.9876 , N \]
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For Trial 4: \[ F_4 = k \frac{|20 \times 10^{-6} \times 8 \times 10^{-6}|}{(0.04)^2} \approx 179.751 , N \]
Responses:
| Trial | Force Calculation | Force | Attraction/Repulsion | |-------|------------------|----------|----------------------| | 1 | \( F \approx 89.876 , N \) | 89.876 N | Repelled | | 2 | \( F \approx 44.938 , N \) | 44.938 N | Repelled | | 3 | \( F \approx 8.9876 , N \) | 8.9876 N | Repelled | | 4 | \( F \approx 179.751 , N \) | 179.751 N | Repelled |
For charges of the same sign:
- All trials will result in repulsion.
Thus, the answers filled in would be:
Column A
- Trial 1: Force = 89.876 N
- Trial 2: Force = 44.938 N
- Trial 3: Force = 8.9876 N
- Trial 4: Force = 179.751 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
Column B
- a. 89.876 N
- d. 44.938 N
- i. 8.9876 N
- h. 179.751 N
- f. Repelled (for all trials)
Question 9 As the value of charge 1 increases, the value of the force increases. So the correct answer is: a. increases; increases.
1 answer