a negative charge of -0.55 uc an unknown charge 0.300 m diectly below it. what are the magnitude an direction of the force that unknown charge exerts on the -0.550 uc charge ?

Well, well, well! We have a negative charge (-0.55 μC) and an unknown charge (0.300 m) directly below it. Let's find out the magnitude and direction of the force between these two charges.

To calculate the force, we can use Coulomb's Law, which states that the force between two charges is given by:

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

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

First, let's convert the charges to coulombs. We have -0.55 μC, which is -0.55 x 10^-6 C, and 0.300 m, which is 0.300 C.

Now, let's substitute the values into the formula:

F = (9 x 10^9 N m^2/C^2) * |(-0.55 x 10^-6 C) * (0.300 C)| / (0.300 m)^2

Simplifying:

F = (9 x 10^9 N m^2/C^2) * (0.165 x 10^-6 C^2) / (0.300 m)^2

Now, let's calculate the magnitude:

F ≈ 27.83 N

So, the magnitude of the force is approximately 27.83 Newtons.

As for the direction, since we have a negative charge (-0.55 μC) above an unknown charge (0.300 m) directly below it, the two charges will attract each other. Therefore, the force between them will be directed upward.

To summarize, the magnitude of the force is approximately 27.83 N, and its direction is upward.

To find the magnitude and direction of the force between two charges, 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.

Here are the given charges and their distances:

Negative charge: -0.55 μC
Unknown charge: 0.300 m below the negative charge

To calculate the force, we need to convert the charges to Coulombs:

Negative charge: -0.55 μC = -0.55 × 10^-6 C
Unknown charge: Convert the distance in meters to centimeters: 0.300 m = 30 cm

Next, let's define the variables:
q1 = magnitude of the negative charge = 0.55 × 10^-6 C
q2 = magnitude of the unknown charge = unknown (will be solved)
r = distance between the charges = 30 cm

Using Coulomb's Law, the formula is:

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

Where k is the Coulomb's constant, k ≈ 8.99 × 10^9 Nm²/C².

Now, let's plug in the values into the formula:

F = (8.99 × 10^9 Nm²/C²) * ( |(-0.55 × 10^-6 C)| * |q2| ) / (30 cm)^2

The magnitude of the force will be the absolute value of the calculated value. The direction of the force will be attractive if the charges are of opposite signs, and repulsive if the charges are of the same sign.

Since we don't have the charge of the unknown charge (q2), we cannot calculate the exact force in this case. If you provide the magnitude or sign of the unknown charge, we can solve for the magnitude and direction of the force.

To find the magnitude and direction of the force that the unknown charge exerts on the negative 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 formula for Coulomb's law is:

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

Where:
F is the force between the two charges,
k is Coulomb's constant (8.99 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, the negative charge has a magnitude of -0.55 μC (microcoulombs), and the unknown charge has a magnitude of 0.300 mC (millicoulombs). The distance between them is given as 0.300 m.

First, convert the charges to the base unit of coulombs:
-0.55 μC = -0.55 x 10^-6 C
0.300 mC = 0.300 x 10^-3 C

Now, substitute the values into the formula:

F = (k * |-0.55 x 10^-6| * |0.300 x 10^-3|) / (0.300)^2

Calculating the magnitude of the force using a calculator:

F ≈ (8.99 x 10^9) * (0.55 x 10^-6) * (0.300 x 10^-3) / (0.300)^2

F ≈ 0.893 x 10^-2 N

The magnitude of the force is approximately 0.893 x 10^-2 N.

Since the unknown charge is located directly below the negative charge, the force will be attractive and directed toward the unknown charge.

Therefore, the magnitude of the force is approximately 0.893 x 10^-2 N, and the direction of the force is downward (toward the unknown charge).