A particle carrying a charge of +32.0 nC is located at (10.0 nm, 95.0 nm), and a particle carrying a charge of +98.0 nC is located at (45.0 nm, 56.0 nm).

Part A
Calculate the magnitude of the electric force exerted on a charged particle placed at the origin if the charge on that particle is 3.90 μC.

Part B
Calculate the magnitude of the electric force exerted on a charged particle placed at the origin if the charge on that particle is 7.15 μC.

Part C
Calculate the magnitude of the electric force exerted on a charged particle placed at the origin if the charge on that particle is 98.1 nC.

Part D
Calculate the magnitude of the electric force exerted on a charged particle placed at the origin if the charge on that particle is -79.5 nC.

Part E
Calculate the magnitude of the electric force exerted on a charged particle placed at the origin if the charge on that particle is 1.00 mC.

Part F
Calculate the magnitude of the electric force exerted on a charged particle placed at the origin if the charge on that particle is 34.1 C.

The magnitude of the electric force exerted on the charged particle at the origin varies depending on the charge of the particle being considered. The results for each case are as follows: A) 0.00367 N, B) 0.00673 N, C) 0.0222 N, D) 0.000593 N, E) 0.367 N, F) 9.91 x [tex]10^{9}[/tex]N

Part A: To calculate the magnitude of the electric force exerted on a charged particle placed at the origin (0, 0) with a charge of 3.90 μC, we can use Coulomb's Law.

Coulomb's Law states that the magnitude of the electric force between two charged particles is given by F = k * (|q1| * |q2|) / r^2, where F is the force, k is the electrostatic constant (9.0 x [tex]10^{9}[/tex] N [tex]m^{2}[/tex]/[tex]C^{2}[/tex]), q1 and q2 are the charges of the particles, and r is the distance between them.

In this case, q1 = 3.90 μC = 3.90 x [tex]10^{-6}[/tex] C, q2 = 32.0 nC = 32.0 x [tex]10^{-9}[/tex] C, and r = distance between (0, 0) and (10.0 nm, 95.0 nm)

= [tex]\sqrt{10nm^{2} + 95nm^{2}[/tex] .

Plugging these values into the formula, we get

F = (9.0 x 10^9 N [tex]m^{2}[/tex]/[tex]C^{2}[/tex]) * ((3.90 x [tex]10^{-6}[/tex] C) * (32.0 x [tex]10^{-9}[/tex] C)) / [tex]\sqrt{10nm^{2} + 95nm^{2}[/tex].

Simplifying the expression gives F ≈ 0.00367 N.

Part B: Following the same procedure as in Part A, with q1 = 7.15 μC = 7.15 x [tex]10^{-6}[/tex] C, q2 = 32.0 nC = 32.0 x [tex]10^{-9}[/tex] C, and the same distance, we obtain F ≈ 0.00673 N.

Part C: Using q1 = 98.1 nC = 98.1 x [tex]10^{-9}[/tex] C, q2 = 32.0 nC = 32.0 x [tex]10^{-9}[/tex] C, and the same distance, we find F ≈ 0.0222 N.

Part D: For q1 = -79.5 nC = -79.5 x [tex]10^{-9}[/tex] C, q2 = 32.0 nC = 32.0 x [tex]10^{-9}[/tex] C, and the same distance, we have F ≈ 0.000593 N.

Part E: Considering q1 = 1.00 mC = 1.00 x [tex]10^{-3}[/tex] C, q2 = 32.0 nC = 32.0 x [tex]10^{-9}[/tex] C, and the same distance, we get F ≈ 0.367 N.

Part F: Finally, with q1 = 34.1 C, q2 = 32.0 nC = 32.0 x [tex]10^{-9}[/tex] C, and the same distance, we obtain F ≈ 9.91 x 10^9 N.

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