A 6 µC charge is placed at the origin and a second

charge is placed on the x-axis at x = 0.34 m.
If the resulting force on the second charge is 4.0 N in the positive x-direction,
what is the value of its charge?

F = k q1 q2 / d^2

To find the value of the second charge, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The mathematical equation for Coulomb's Law is:

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

Where:
F is the magnitude of the force between the two charges,
k is Coulomb's constant, approximately equal to 9.0 x 10^9 N·m^2/C^2,
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.

In this case, we are given:

|q1| = 6 µC = 6 x 10^-6 C (The charge at the origin)
|q2| = Unknown (The charge on the x-axis)
F = 4.0 N (The resulting force)
r = 0.34 m (Distance between the charges)

Let's substitute these values into the equation:

4.0 N = (9.0 x 10^9 N·m^2/C^2) * ((6 x 10^-6 C) * |q2|) / (0.34 m)^2

Now, solve for |q2|:

|q2| = (4.0 N * (0.34 m)^2) / (9.0 x 10^9 N·m^2/C^2 * 6 x 10^-6 C)

Calculating this expression will give us the value of |q2|, which is the magnitude of the second charge.

To find the value of the second charge, we can use Coulomb's Law:

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

where F is the force between the charges, k is the electrostatic constant (9.0 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between them.

In this case, we know the following:

F = 4.0 N
k = 9.0 x 10^9 N m^2/C^2
q1 = 6 µC (6 x 10^-6 C)
r = 0.34 m

Substituting the values into the equation, we have:

4.0 N = (9.0 x 10^9 N m^2/C^2) * (6 x 10^-6 C) * |q2| / (0.34 m)^2

Simplifying, we get:

4.0 N = (54 x 10^3 C^2) * |q2| / (0.1156 m^2)

Now, let's solve for |q2|:

|q2| = (4.0 N * (0.1156 m^2)) / (54 x 10^3 C^2)
|q2| = 0.0086 C

Therefore, the value of the second charge is approximately 0.0086 C.