A 6.6-μC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.1 m.If the resulting force on the second charge is 5.7 N in the positive x-direction,what is the value of its charge?
A)1.0 μC
B)1.0 nC
C)-1.0 μC
D)-1.0 nC
E)0 μC

Question

A 6.6-μC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.1 m.If the resulting force on the second charge is 5.7 N in the positive x-direction,what is the value of its charge?​
A)1.0 μC
B)1.0 nC
C)-1.0 μC
D)-1.0 nC
E)​0 μC

Quizplus · Accepted Answer

The force between two charges is given by Coulomb's law, $F = k \frac{|q_1 q_2|}{r^2}$, where $k = 8.987 \times 10^9 \, \text{N m}^2/\text{C}^2$, $q_1$ and $q_2$ are the charges, and $r$ is the distance between them. Given $F = 5.7 \, \text{N}$, $q_1 = 6.6 \, \mu\text{C} = 6.6 \times 10^{-6} \, \text{C}$, and $r = 0.1 \, \text{m}$, we can solve for $q_2$. The direction of the force indicates that $q_2$ has the same sign as $q_1$, making it positive. Solving for $q_2$ gives a value close to $1.0 \, \mu\text{C}$, indicating that the charges repel each other, consistent with them having the same sign.

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