Introduction to Electrostatic Force
Understanding Coulomb's Law and Its Application
Coulomb's Law is a fundamental principle in electrostatics that describes the interaction between two point charges in a vacuum. The law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The mathematical representation of this is given by:
Coulomb's Law Equation
F k (frac{q_1 q_2}{r^2})
F is the electrostatic force between the charges, measured in Newtons (N). (k) is Coulomb's constant, approximately (8.99 times 10^9 , text{N m}^2/text{C}^2). (q_1) and (q_2) are the magnitudes of the charges, measured in Coulombs (C). (r) is the distance between the charges, measured in meters (m).This equation is widely used in physics to solve problems involving the interaction between charged particles.
Solving for Identical Charges with Known Forces and Distance
The problem at hand involves finding the size of each charge given the electrostatic force and the distance between them. Let’s break down the steps to find the charge.
Given Information
Electrostatic force ((F)) 1.3 N Distance ((r)) 36 mm 0.036 m Identical charges ((q_1 q_2 q))Step-by-Step Solution
Since the charges are identical, the equation simplifies to: [text{F} text{k} frac{q^2}{r^2}] Substituting the known values: [begin{align*}text{F} 1.3 , text{N} text{k} 8.99 times 10^9 , text{N m}^2/text{C}^2 text{r} 0.036 , text{m} end{align*}] Computing (r^2): [text{r}^2 (0.036)^2 0.001296 , text{m}^2] Substituting (r^2) and (F) into the simplified Coulomb's Law equation: [begin{align*}1.3 8.99 times 10^9 times frac{q^2}{0.001296} frac{1.3 times 0.001296}{8.99 times 10^9} q^2 frac{0.0016848}{8.99 times 10^9} q^2 frac{1.87 times 10^{-13}}{1} q^2 end{align*}] Calculating (q) by taking the square root: [q sqrt{1.87 times 10^{-13}} approx 1.37 times 10^{-7} , text{C}]Hence, the size of each charge is approximately 1.37 (times) 10(^{-7}) C.
Conclusion
Coulomb's Law is a powerful tool for understanding and calculating the electrostatic force between charged particles. By mastering this equation, you can tackle a wide array of problems in physics. Understanding the basics of this law is crucial for all students and professionals in the field of physics and engineering.