Math Problem Statement
Given two charges q1=5 μC and q2=−5 μC are separated by a distance r in a vacuum. If the magnitude of the force between them is 1 N, what is the separation distance r? a) 1.5 m b) 0.1 m c) 0.3 m d) 0.5 m
Solution
To find the separation distance between the charges and , we can use Coulomb's Law, which states that the force between two charges is given by:
where:
- is the magnitude of the force between the charges,
- is Coulomb's constant (),
- and are the magnitudes of the charges,
- is the separation distance between the charges.
Given:
- ,
- ,
- .
Let's solve for :
First, simplify the numerator:
Now substitute back into the equation:
Now, solve for :
Comparing this to the given options:
a) 1.5 m
b) 0.1 m
c) 0.3 m
d) 0.5 m
The closest answer is .
Thus, the separation distance is approximately .
Would you like more details or have any questions?
Here are five more questions you might want to ask:
- How do you derive Coulomb's Law?
- What are the units of Coulomb's constant ?
- Can you explain how to convert microcoulombs to coulombs?
- What are some applications of Coulomb's Law in real life?
- How does the force between charges change if one of the charges is doubled?
Tip: Always ensure that the units are consistent when using formulas in physics to avoid calculation errors.
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Math Problem Analysis
Mathematical Concepts
Electric Charge
Coulomb's Law
Formulas
Coulomb's Law: F = k * |q1 * q2| / r^2
Theorems
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Suitable Grade Level
Grades 11-12