A -4.0UC charge is located 0.45m to the left of a +6.0uc charge. what is the magnitude and direction of the electrostatic force on the positive charge?
F=k•(q1•q2)/r^2=9•10^9•(4•10^-6•6•10^-6)/(0.45)^2=1.067N
2.2N
To solve this problem, we can use Coulomb's Law, which describes the electrostatic force between two charged objects. The formula for Coulomb's Law is:
F = k * |q1 * q2| / r^2
Where:
- F is the electrostatic force
- k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2)
- q1 and q2 are the magnitudes of the charges
- r is the distance between the charges
Given:
q1 = +6.0 μC (positive charge)
q2 = -4.0 μC (negative charge)
r = 0.45 m
Now, let's calculate the electrostatic force:
F = (8.99 x 10^9 Nm^2/C^2) * |(+6.0 μC) * (-4.0 μC)| / (0.45 m)^2
First, we'll calculate the magnitude of the force:
|(+6.0 μC) * (-4.0 μC)| = 6.0 μC * 4.0 μC = 24.0 μC^2
Now, substitute the values into the formula:
F = (8.99 x 10^9 Nm^2/C^2) * (24.0 μC^2) / (0.45 m)^2
Simplifying further:
F = (8.99 x 10^9 Nm^2/C^2) * (24.0 x 10^-12 C^2) / (0.45 m)^2
F ≈ 3.03 x 10^-6 N
Now that we have the magnitude of the force, let's determine its direction. Since the negative charge (-4.0 μC) is to the left of the positive charge (+6.0 μC), the electrostatic force will be attractive and act towards the negative charge. Therefore, the direction of the electrostatic force on the positive charge is to the left.
To find the magnitude and direction of the electrostatic force on the positive charge, we can use Coulomb's law. Coulomb's law states that the magnitude of the electrostatic force between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between the charges.
The formula for Coulomb's law is as follows:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the magnitude of the electrostatic force.
- k is the electrostatic constant, approximately 9.0 x 10^9 Nm^2/C^2.
- q1 and q2 are the magnitudes of the charges (in microcoulombs, uc).
- r is the distance between the charges (in meters, m).
Let's substitute the given values into the formula:
F = (9.0 x 10^9 Nm^2/C^2) * (|6.0 uc| * |-4.0 uc|) / (0.45 m)^2
First, let's calculate the product of the magnitudes of the charges: |6.0 uc| * |-4.0 uc| = 24.0 uc^2.
Now let's substitute all the values into the formula:
F = (9.0 x 10^9 Nm^2/C^2) * (24.0 uc^2) / (0.45 m)^2
Simplifying further:
F = (9.0 x 10^9 Nm^2/C^2) * 24.0 uc^2 / (0.2025 m^2)
F = 216.0 x 10^9 Nuc / 0.2025 m^2
F = 1069.14 x 10^9 Nuc / m^2
The magnitude of the electrostatic force on the positive charge is approximately 1.07 x 10^12 Nuc / m^2.
To determine the direction of the force, we can apply the principle that like charges repel each other. Since the charges have the same sign (+6.0 uc and +4.0 uc), the electrostatic force will act away from the -4.0 uc charge.
Therefore, the magnitude of the electrostatic force on the positive charge is approximately 1.07 x 10^12 Nuc / m^2, and the direction is away from the -4.0 uc charge.