1------- A -10 uC charge is placed 0.20 m away from an unknown charge. The force between the two charges is found to be attractive and has a value of 9.0 N. What is the magnitude and sign of the other charge?

2-------- A -5 uC charge is a distance of 12 cm from a 7 uC charge. What is the magnitude of the force between the two charges? is the force attractive or repulsive?

Thank you!

To find the magnitude and sign of the unknown charge in question 1, we can use Coulomb's law:

Coulomb's law states that the force between two charged objects is given by the equation:

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

where
F is the force between the charges,
k is the electrostatic constant (k = 8.99 × 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 question 1, we are given:
|q1| = 10 μC = 10 × 10^(-6) C
F = 9.0 N
r = 0.20 m

Plugging in the given values into the equation, we can solve for |q2|:

9.0 N = (8.99 × 10^9 N m^2/C^2) * (10 × 10^(-6) C * |q2|) / (0.20 m)^2

Simplifying the equation:

9.0 N = (8.99 × 10^9 N m^2/C^2) * (10 × 10^(-6) C^2) / (0.20 m)^2 * |q2|

Now, solve for |q2|:

|q2| = (9.0 N * (0.20 m)^2) / (8.99 × 10^9 N m^2/C^2 * 10 × 10^(-6) C)= 0.08 C

So, the magnitude of the other charge is 0.08 C. The force between the two charges is attractive because the given force is positive.

Moving on to question 2:

Using Coulomb's law:

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

where
|q1| = 5 μC = 5 × 10^(-6) C
|q2| = 7 μC = 7 × 10^(-6) C
r = 12 cm = 0.12 m
k = 8.99 × 10^9 N m^2/C^2

Plugging in the given values into the equation, we can calculate the force:

F = (8.99 × 10^9 N m^2/C^2) * (5 × 10^(-6) C * 7 × 10^(-6) C) / (0.12 m)^2

F = (8.99 × 10^9 N m^2/C^2) * (35 × 10^(-12) C^2) / (0.0144 m^2)

Simplifying the equation:

F = (8.99 × 10^9 N m^2/C^2) * (35 × 10^(-12) C^2) / (1.44 × 10^(-2) m^2)

F ≈ 221.09 N

Therefore, the magnitude of the force between the charges is approximately 221.09 N. The force between them is attractive because the charges have opposite signs.

1------- To find the magnitude and sign of the other charge, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. The formula for Coulomb's law is:

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

Where:
F is the force between the charges,
k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.

In this case, we have an attractive force (given by the negative sign on the charge). Plugging the given values into the formula, we have:

9.0 N = (9 x 10^9 Nm^2/C^2) * (10^-6 C) * |q2| / (0.20 m)^2

Simplifying the equation, we have:

9.0 N = (9 x 10^9 Nm^2/C^2) * (10^-6 C) * |q2| / 0.04 m^2

9.0 N = (9 x 10^3 C) * (10^-6 C) * |q2|

9.0 N = 9 * |q2|

Dividing both sides by 9, we get:

1.0 N = |q2|

Therefore, the magnitude of the other charge is 1.0 Coulomb and the sign can be determined as positive because it is attractive to the negative charge.

2-------- To find the magnitude of the force between the two charges, we can again use Coulomb's law. Plugging the given values into the formula:

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

F = (9 x 10^9 Nm^2/C^2) * (5 x 10^-6 C) * (7 x 10^-6 C) / (0.12 m)^2

F = (9 x 10^9 Nm^2/C^2) * (5 x 7 x 10^-12) / 0.0144 m^2

F = (315 x 10^-12) / (0.0144 m^2)

F = 2.18 x 10^-8 N

Therefore, the magnitude of the force between the charges is 2.18 x 10^-8 N. The force can be determined as repulsive because both charges have the same sign (both negative in this case).