Figure (a) shows charged particles 1 and 2 that are fixed in place on an x axis. Particle 1 has a charge with a magnitude of |q1| = 12.0e. Particle 3 of charge q3 = +13.0e is initially on the x axis near particle 2. Then particle 3 is gradually moved in the positive direction of the x axis. As a result, the magnitude of the net electrostatic force on particle 2 due to particles 1 and 3 changes.

Figure (b) gives the x component of that net force as a function of the position x of particle 3. The scale of the x axis is set by xs = 1.70 m. The plot has an asymptote of F2,net = 1.370 × 10-25 N as x → ∞.

As a multiple of e and including the sign, what is the charge q2 of particle 2?

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To determine the charge q2 of particle 2, we need to analyze the given information and figure (b).

From figure (b), we can see that as the position x of particle 3 increases, the x-component of the net electrostatic force on particle 2 approaches a constant value of 1.370 × 10^-25 N, denoted as F2,net.

The x-component of the net electrostatic force on particle 2 can be calculated using Coulomb's Law, which states:

F2,net = k * |q1*q2| / r^2

where k is the electrostatic constant, q1 is the charge of particle 1, q2 is the charge of particle 2, and r is the distance between particles 1 and 2.

Since particle 1 and 2 are fixed in place, the distance r remains constant. Therefore, the only variable factor affecting the net force is the charge q2.

From figure (b), we can see that as x → ∞, the force F2,net approaches a constant value. This implies that as x → ∞, the product |q1*q2| remains constant.

Since we know that |q1| = 12.0e and |q3| = 13.0e, the product |q1*q2| = |q3*q2| remains constant as x → ∞.

Taking the limit as x → ∞, we have:

|q1*q2| = |q3*q2| = 13.0e*q2 = 1.370 × 10^-25 N * r^2

Now, we can solve for q2:

q2 = (1.370 × 10^-25 N * r^2) / 13.0e

Substituting r = xs = 1.70 m and e = elementary charge = 1.602 × 10^-19 C, we can calculate q2:

q2 = (1.370 × 10^-25 N * (1.70 m)^2) / (13.0 * 1.602 × 10^-19 C)

Calculating this expression gives us the value of q2 as a multiple of e.

To find the charge, q2, of particle 2, we need to analyze the given information in Figure (b).

First, let's understand the graph in Figure (b). It shows the x-component of the net electrostatic force on particle 2 as a function of the position, x, of particle 3. The x-axis represents the position of particle 3, and the y-axis represents the x-component of the net force on particle 2. The graph has an asymptote at F2,net = 1.370 × 10^-25 N as x → ∞.

From the graph, we can see that as particle 3 moves in the positive direction of the x-axis, the magnitude of the net electrostatic force on particle 2 changes. This indicates that there is a changing electrostatic interaction between particles 1 and 3, resulting in a changing force on particle 2.

To find the charge of particle 2, we need to find the value of q2 that corresponds to the x-coordinate where the force approaches the asymptote. Let's find that point on the graph.

We know that the force on particle 2 approaches 1.370 × 10^-25 N as x → ∞. To find the x-coordinate for this point on the graph, we need to locate where the curve approaches the asymptote. From the graph, it looks like this occurs at x = 1.70 m.

Now, we need to find the corresponding value of the force on particle 2 at x = 1.70 m. From the graph, it appears to be at approximately -5.0 × 10^-25 N.

Next, we can use Coulomb's law to find the charge of particle 2. Coulomb's law states that the magnitude of the force between two charged particles is given by:

|F| = k * |q1| * |q2| / r^2

where |F| is the magnitude of the force, k is the electrostatic constant, |q1| and |q2| are the magnitudes of the charges, and r is the distance between the particles.

In this case, the magnitude of the force at x = 1.70 m is given by:
|F| = 5.0 × 10^-25 N

The distance between particle 1 and 2 is fixed, so we can assume r is constant.

The electrostatic constant, k, is approximately equal to 9 × 10^9 Nm^2/C^2.

Plugging in the values into the formula, we can now solve for |q2|:

5.0 × 10^-25 N = (9 × 10^9 Nm^2/C^2) * 12.0e * |q2| / (fixed value of r)^2

Simplifying the equation further, divide both sides by the constants:

|q2| = (5.0 × 10^-25 N) * (fixed value of r)^2 / (9 × 10^9 Nm^2/C^2 * 12.0e)

Now, you can calculate the value of |q2| by substituting the fixed value of r into the equation and calculating the expression.

Thus, as a multiple of e and including the sign, you can find the charge, q2, of particle 2 by substituting the values into the formula and calculating the expression.

As x-> infinity, it no longer affects the force on particle 2, F2.

Use the value of F2 when x = infinity, the fixed distance separation of 1 and 2, and Coulomb's equation to determine the charge of particle 2.

As above, as the x-value for particle 3 approaches infinity the only force acting on particle 2 is from particle 1. The asymptote is the value of that force. Set the equation for (kq1q2)/(r^2) = 1.370e-25N and solve for q2.

Note that you can solve for r with the knowledge that the Fnet provided is the constant force from q1 onto q2 and that the net force is 0 at the x-value where the graph crosses the x axis.