To calculate the force between two point charges, we can use Coulomb's Law, which is given by the formula:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
where:
- \( F \) is the force between the charges,
- \( k = \frac{1}{4\pi \epsilon_0} \) is the Coulomb's constant (given as \( 9 \times 10^9 , \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the charges,
- \( r \) is the distance between the charges.
Given:
- \( q_1 = 3 \times 10^{-6} , \text{C} \)
- \( q_2 = 4 \times 10^{-8} , \text{C} \)
- \( r = 4 , \text{cm} = 0.04 , \text{m} \)
Now, we can substitute these values into Coulomb's Law:
-
Calculate the product of the charges: \[ |q_1 q_2| = |(3 \times 10^{-6}) (4 \times 10^{-8})| = 12 \times 10^{-14} , \text{C}^2 \]
-
Calculate \( r^2 \): \[ r^2 = (0.04)^2 = 0.0016 , \text{m}^2 \]
-
Now plug in the values into Coulomb's Law: \[ F = 9 \times 10^9 \frac{12 \times 10^{-14}}{0.0016} \]
-
Calculate the fraction: \[ \frac{12 \times 10^{-14}}{0.0016} = \frac{12 \times 10^{-14}}{1.6 \times 10^{-3}} = 7.5 \times 10^{-11} \]
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Now calculate \( F \): \[ F = 9 \times 10^9 \times 7.5 \times 10^{-11} = 6.75 \times 10^{-1} , \text{N} = 0.675 , \text{N} \]
Thus, the force between the two charges is 0.675 N.