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 on a 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 magnitudes, and inversely proportional to the square of the distance between them.
(a) To find the magnitude of the electrostatic force on the 10 microCoulomb charge, we first need to calculate the distance between the two charges. The 10 microCoulomb charge is located at the origin (0,0), and the 3 microCoulomb charge is located at (1,-2). Using the distance formula, we have:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((1 - 0)^2 + (-2 - 0)^2)
= sqrt(1 + 4)
= sqrt(5) units
Now, we can use Coulomb's Law to calculate the magnitude of the electrostatic force. Coulomb's Law formula is:
Force = (k * |q1 * q2|) / r^2
where k is the electrostatic constant (k = 9 * 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between them.
Plugging in the given values, we have:
Force = (9 * 10^9 N m^2/C^2) * |10 * 10^(-6) C * 3 * 10^(-6) C| / (sqrt(5))^2
= (9 * 10^9 N m^2/C^2) * (30 * 10^(-12) C^2) / 5
= (9 * 10^9 N m^2/C^2) * 6 * 10^(-12) C^2 / 5
= (54 * 10^(-9)) / 5
= 10.8 * 10^(-9) N
Therefore, the magnitude of the electrostatic force on the 10 microCoulomb charge is 10.8 * 10^(-9) N.
(b) To find the force on the 3 microCoulomb charge, we can use the fact that the force between two charges is equal and opposite. Therefore, the force on the 3 microCoulomb charge will have the same magnitude as the force on the 10 microCoulomb charge but in the opposite direction.
In component notation, the force on the 3 microCoulomb charge is:
F = -10.8 * 10^(-9) N, or in vector form, F = (-10.8 * 10^(-9) N, 0).