1. What is (a)the magnitude of the electrostatic force on a 10 microCoulomb charge located at the origin due to a 3 microCoulomb charge located at 1,-2? (b) What is the force on the 3 microCoulomb charge? Write your answer in component notation.
To find the magnitude of the electrostatic force between two charges, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's solve this problem step by step:
(a) To find the magnitude of the electrostatic force on the 10 microCoulomb charge (q1) at the origin due to the 3 microCoulomb charge (q2) at the coordinates (1, -2), we can use Coulomb's Law:
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 distance between the charges.
First, let's calculate the distance between the two charges using the distance formula:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given that q1 is at the origin (0, 0) and q2 is at (1, -2), we have:
r = sqrt((1 - 0)^2 + (-2 - 0)^2)
= sqrt(1 + 4)
= sqrt(5)
Now we can substitute the values into Coulomb's Law:
F = (8.99 x 10^9 Nm^2/C^2) * ((10 x 10^-6 C) * (3 x 10^-6 C)) / (sqrt(5))^2
Simplifying the equation:
F = (8.99 x 10^9 Nm^2/C^2) * (30 x 10^-12 C^2) / 5
F = (8.99 x 10^9 Nm^2/C^2) * 6 x 10^-12 C^2
F = 53.94 N
Therefore, the magnitude of the electrostatic force on the 10 microCoulomb charge is 53.94 Newtons.
(b) To find the force on the 3 microCoulomb charge, we can use Newton's third law, which states that the force between two charges is equal in magnitude but opposite in direction. So, the force on the 3 microCoulomb charge will be the same as the force on the 10 microCoulomb charge but in the opposite direction.
Therefore, the force on the 3 microCoulomb charge is -53.94 N in component notation.
Answer:
(a) The magnitude of the electrostatic force on the 10 microCoulomb charge is 53.94 Newtons.
(b) The force on the 3 microCoulomb charge in component notation is -53.94 N.