The force between charges is illustrated by Coulomb's law. The force exerted on charge 3 by the first and second charge is [tex]-2.38 \times 10^{-5}N[/tex]
The force between charges is calculated using:
[tex]F = k\frac{q_1q_2}{r^2}[/tex]
Where:
[tex]k=8.9875 \times 10^9 Nm^2C^{-2}[/tex]
The given parameters are:
[tex]q_1 = -10nC[/tex] at [tex]x_1 = -1.67m[/tex]
[tex]q_2 = 32.5nC[/tex] at [tex]x_2 = 0m[/tex]
[tex]q_3 = 47.0nC[/tex] at [tex]x_3 = -1.075m[/tex]
Calculate the distance between the first and third charges
[tex]d_{13} = x_1 - x_3[/tex]
[tex]d_{13} = -1.67m - -1.075m[/tex]
[tex]d_{13} = -0.595m[/tex]
The force between the first and third charges is:
[tex]F_{13} = k\frac{q_1q_3}{d_{13}^2}[/tex]
So, we have:
[tex]F_{13} = 8.9875 \times 10^9 \times \frac{-10nC \times 47nC}{(-0.595)^2}[/tex]
[tex]F_{13} = 8.9875 \times 10^9 \times \frac{-10\times 10^{-9} \times 47 \times 10^{-9}}{(-0.595)^2}[/tex]
[tex]F_{13} = -1.19 \times 10^{-5}N[/tex]
Calculate the distance between the second and third charges
[tex]d_{23} = x_2 - x_3[/tex]
[tex]d_{23} = 0m - -1.075m[/tex]
[tex]d_{23} = 1.075m[/tex]
The force between the second and third charges is:
[tex]F_{23} = k\frac{q_2q_3}{d_{23}^2}[/tex]
So, we have:
[tex]F_{23} = 8.9875 \times 10^9 \times \frac{32.5nC \times 47nC}{(1.075)^2}[/tex]
[tex]F_{23} = 8.9875 \times 10^9 \times \frac{32.5\times 10^{-9} \times 47 \times 10^{-9}}{(1.075)^2}[/tex]
[tex]F_{23} = 1.189 \times 10^{-5}N[/tex]
The net force is then calculated as follows:
[tex]F_{net3}x = F_{13} - F_{23}[/tex]
This gives:
[tex]F_{net3}x = - 1.19 \times 10^{-5}N - 1.19 \times 10^{-5}N[/tex]
[tex]F_{net3}x = - 2.38 \times 10^{-5}N[/tex]
Hence, the net force on the third charge is [tex]-2.38 \times 10^{-5}N[/tex]
Read more about net forces at:
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