What is the electrostatic force between two point charges of +1 nC and -1 nC placed 1 m apart?
Understand the Problem
The question is asking for the calculation of the electrostatic force between two point charges, one positive and one negative, separated by a distance of 1 meter. This can be solved using Coulomb's law, which relates the force to the magnitudes of the charges and the distance between them.
Answer
The electrostatic force is \( F = 8.99 \times 10^{-9} \, \text{N} \).
Answer for screen readers
The electrostatic force between the two point charges is ( F = 8.99 \times 10^{-9} , \text{N} ).
Steps to Solve
- Identify the Values We need to identify the values given in the problem:
- Charge 1 ($q_1$): $+1 , \text{nC} = 1 \times 10^{-9} , \text{C}$
- Charge 2 ($q_2$): $-1 , \text{nC} = -1 \times 10^{-9} , \text{C}$
- Distance ($r$): $1 , \text{m}$
- Apply Coulomb's Law Coulomb's Law states that the electrostatic force ($F$) between two point charges is given by the formula:
$$ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} $$
where $k$ is Coulomb's constant, approximately $8.99 \times 10^9 , \text{N m}^2/\text{C}^2$.
- Substituting the Values Substituting the values into the formula:
$$ F = 8.99 \times 10^9 \cdot \frac{|(1 \times 10^{-9}) \cdot (-1 \times 10^{-9})|}{(1)^2} $$
- Calculate the Force Now calculate the force:
$$ F = 8.99 \times 10^9 \cdot \frac{1 \times 10^{-18}}{1} = 8.99 \times 10^{-9} , \text{N} $$
The force is attractive since the charges are opposite.
The electrostatic force between the two point charges is ( F = 8.99 \times 10^{-9} , \text{N} ).
More Information
This result shows the attractive force between a positive and a negative charge, where the magnitude of the force is very small due to the small size of the charges involved (nanoCoulombs). Coulomb's law is fundamental in electrostatics, highlighting how charged objects interact over a distance.
Tips
- Confusing the signs of the charges: Always remember that opposite charges attract and like charges repel.
- Misplacing Coulomb's constant: Ensure that you use the correct value for $k = 8.99 \times 10^9 , \text{N m}^2/\text{C}^2$.
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