At what separation is the electrostatic force between a +11.5 \mu C point charge and a +29.2 \mu C point charge equal in magnitude to 1.90 N?

To find the separation at which the electrostatic force between the two point charges is equal to 1.90 N, we can use Coulomb's law:

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

where F is the electrostatic force, k is the electrostatic constant (9.0 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the separation between the charges.

In this case, we have:
F = 1.90 N
q1 = +11.5 μC = 11.5 x 10^-6 C
q2 = +29.2 μC = 29.2 x 10^-6 C
k = 9.0 x 10^9 Nm^2/C^2

We can rearrange Coulomb's law to solve for r:

r = sqrt(k * |q1 * q2| / F)

Substituting the given values:

r = sqrt((9.0 x 10^9 Nm^2/C^2) * (11.5 x 10^-6 C) * (29.2 x 10^-6 C) / (1.90 N))

Calculating the expression:

r = sqrt((3.168 x 10^-3 Nm^2/C^2) / (1.90 N))

r = sqrt(1.665 x 10^-3 m^2)

r = 4.082 x 10^-2 m

Therefore, the separation at which the electrostatic force between the +11.5 μC and +29.2 μC charges is equal to 1.90 N is approximately 0.04082 m (or 4.082 cm).

To find the separation at which the electrostatic force between two charges is equal to 1.90 N, we can use Coulomb's law, which states that the electrostatic force between two point charges is given by:

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

where F is the force, k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the separation between the charges.

In this case, we have a +11.5 μC (microcoulomb) point charge and a +29.2 μC (microcoulomb) point charge. Let's denote q1 as +11.5 x 10^-6 C and q2 as +29.2 x 10^-6 C. The force is given as 1.90 N.

To find the separation (r), we rearrange Coulomb's law and solve for r:

r = sqrt((k * |q1 * q2|) / F)

Now let's plug in the values:

r = sqrt((8.99 x 10^9 Nm^2/C^2 * |(+11.5 x 10^-6 C) * (+29.2 x 10^-6 C)|) / 1.90 N)

r = sqrt((8.99 x 10^9 Nm^2/C^2 * (11.5 x 10^-6 C * 29.2 x 10^-6 C)) / 1.90 N)

r = sqrt((8.99 x 10^9 Nm^2/C^2 * 336.8 x 10^-12 C^2) / 1.90 N)

r = sqrt((3.032432 x 10^-2 Nm^2/C^2) / 1.90 N)

r = sqrt(1.594444 x 10^-2 m^2)

r = 0.126 m

Therefore, the separation at which the electrostatic force between the +11.5 μC and +29.2 μC point charges is equal to 1.90 N is approximately 0.126 m.

Solve the Coulomb's Law equation for separation distance, R.

1.90 N = k*Q1*Q2/R^2