Respuesta :
Answer:
Explanation:
Given
Charge [tex]q_3=+5\ nC[/tex] is placed at origin
Charge [tex]q_2=-3\ nC[/tex] is placed at [tex]x=5\ cm[/tex]
Charge [tex]q_1[/tex] is Placed at [tex]x=2.5\ cm[/tex]
charge [tex]q_1[/tex] must be positive so as to balance the force on charge [tex]q_3[/tex]
Force on [tex]q_3[/tex] due to [tex]q_1[/tex] is
[tex]F_{31}=\frac{kq_1q_3}{r^2}[/tex]
here [tex]r=2.5\ cm[/tex]
[tex]F_{31}=\frac{kq_1q_3}{(2.5)^2}[/tex]
Force on [tex]q_3[/tex] due to [tex]q_2[/tex] is
[tex]F_{32}=\frac{kq_3q_2}{r^2}[/tex]
here [tex]r=5\ cm[/tex]
[tex]F_{32}=\frac{kq_3q_2}{(5)^2}[/tex]
[tex]F_{31}=F_{32}[/tex]
[tex]\frac{kq_1q_3}{(2.5)^2}=\frac{kq_3q_2}{(5)^2}[/tex]
[tex]q_1=q_2(\frac{2.5}{5})^2[/tex]
[tex]q_1=3\times (\frac{2.5}{5})^2[/tex]
[tex]q_1=3\times \frac{1}{4}[/tex]
[tex]q_1=0.75\ nC[/tex]
The magnitude and sign of charge [tex]q_1[/tex] is equal to +0.75 nC.
Given the following data:
- Charge [tex]q_3[/tex] = +5.00 nC.
- Radius of [tex]q_3[/tex] = origin.
- Charge [tex]q_2[/tex] = -3.00 nC.
- Radius of [tex]q_2[/tex] = 5.00 cm.
- Radius of [tex]q_1[/tex] = 2.50 cm.
How to calculate electrostatic force.
Mathematically, the electrostatic force between two (2) charges is given by this formula:
[tex]F = k\frac{q_1q_2}{r^2}[/tex]
Where:
- q represent the charge.
- r is the distance between two charges.
- k is Coulomb's constant.
The electrostatic force between charges 2 and 3 is given by:
[tex]F_{23} = k\frac{q_2q_3}{r^2_{23}}[/tex] .....equation 1.
The electrostatic force between charges 1 and 3 is given by:
[tex]F_{13} = k\frac{q_1q_3}{r^2_{13}}[/tex] .....equation 2.
Since [tex]F_{23}[/tex] is pointing in the +x direction, [tex]F_{13}[/tex] has to point in the -x direction and as such charge [tex]q_1[/tex] must have a positive charge.
Equating eqn. 2 and eqn. 1, we have:
[tex]k\frac{q_2q_3}{r^2_{23}}= k\frac{q_1q_3}{r^2_{13}}\\\\q_1=q_2(\frac{r^2_{13}}{r^2_{23}} )[/tex]
Substituting the given parameters into the equation, we have;
[tex]q_1=3 \times \frac{2.50^2}{5.00^2} \\\\q_1=3 \times \frac{6.25}{25}\\\\q_1=3 \times 0.25[/tex]
Charge 1 = +0.75 nC.
Read more on charges here: brainly.com/question/4313738
