Charge A, +1 μC, is positioned at the origin of a coordinate system as shown below. Charge B, −1 μC, is fixed at x = 3 m.
(a) Determine the magnitude and direction of the force that charge B exerts on charge A.
(b) What is the force that charge A exerts on charge B?
To find the force between two charges, we can use Coulomb's Law. The formula for Coulomb's Law is:
F = k * |q1 * q2| / r^2
Where:
F is the force between the two charges,
k is the electrostatic constant (approximately equal to 9 × 10^9 N m^2/C^2),
q1 and q2 are the magnitudes of the two charges, and
r is the distance between the charges.
(a) To find the magnitude and direction of the force that charge B exerts on charge A, we can substitute the given values into Coulomb's Law.
Charge A, q1 = +1 μC = 1 × 10^(-6) C
Charge B, q2 = -1 μC = -1 × 10^(-6) C
Distance between the charges, r = 3 m
Electrostatic constant, k = 9 × 10^9 N m^2/C^2 (given)
Substituting these values into the formula, we have:
F = (9 × 10^9 N m^2/C^2) * |(1 × 10^(-6) C) * (-1 × 10^(-6) C)| / (3 m)^2
Simplifying further:
F = (9 × 10^9 N m^2/C^2) * (1 × 10^(-12) C^2) / (9 m^2)
F = 1 N
The magnitude of the force is 1 N, and since charge B is negative, the force will be attractive toward charge B. Therefore, the direction of the force that charge B exerts on charge A is toward charge B.
(b) The force that charge A exerts on charge B is equal in magnitude but opposite in direction to the force that charge B exerts on charge A. So, the force that charge A exerts on charge B is also 1 N, but the direction will be opposite, away from charge B.
F = kq1q2/r^2 = 9e9*1e-6*-1e-6/3^2.
They exert the same force on each other (but opposite directions)