The force of electrostatic repulsion between two small positively charged objects, A and B, is 3.6 x 10⁻⁵ N when AB = 0.12m. What is the force of repulsion if AB is increased to 0.24 m

Respuesta :

Given data:

* The electrostatic force of repulsion between the charged bodies in the initial state is,

[tex]F=3.6\times10^{-5}\text{ N}[/tex]

* The distance between the charged bodies in the initial state is,

[tex]d=0.12\text{ m}[/tex]

* The distance between the charged bodies in the final state is,

[tex]\begin{gathered} d^{\prime}=0.24\text{ m} \\ d=2\times0.12 \\ d^{\prime}=2d \end{gathered}[/tex]

Solution:

According to Coulomb's law, the electrostatic force of repulsion between the charged bodies in the initial state is,

[tex]F=\frac{kq_1q_2}{d^2}[/tex]

where k is the electrostatic force constant, q_1 is the charge on the first charged body and q_2 is the charge on the second charged body,

The electrostatic force of repulsion between the charged bodies in the final state is,

[tex]\begin{gathered} F^{\prime}=\frac{kq_1q_2}{(2d)^2} \\ F^{\prime}=\frac{kq_1q_2}{4d^2} \\ F^{\prime}=\frac{1}{4}\times\frac{kq_1q_2}{d^2} \\ F^{\prime}=\frac{F}{4} \end{gathered}[/tex]

Substituting the known values,

[tex]\begin{gathered} F^{\prime}=\frac{3.6\times10^{-5}}{4} \\ F^{\prime}=0.9\times10^{-5}\text{ N} \end{gathered}[/tex]

Thus, the electrostatic force of repulsion between the charged bodies in the final state is,

[tex]\text{0}.9\times10^{-5}\text{ N}[/tex]