Three charges are fixed in the x−y plane as follows: 1.5nC at the origin (0, 0); 2.6nC at (0.65m , 0); –1.8nC nC at (0, 1.50m ).
Find the force acting on the charge at the origin.
Express your answers using two significant figures. Enter the x and y components of the force separated by a comma.
To find the force acting on the charge at the origin, we can use Coulomb's Law, which 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.
First, calculate the distance between the charge at the origin and the charge at (0.65m, 0). Since the two charges are on the x-axis, the distance between them is the difference in their x-coordinates.
Distance = (0.65 m - 0 m) = 0.65 m
Next, calculate the distance between the charge at the origin and the charge at (0, 1.50 m). Since the two charges are on the y-axis, the distance between them is the difference in their y-coordinates.
Distance = (1.50 m - 0 m) = 1.50 m
Now, we can calculate the force between the charge at the origin and the charge at (0.65 m, 0) using Coulomb's Law:
Force_1 = (k * |q1 * q2|) / d^2
where k is the electrostatic constant (8.99 * 10^9 N m^2 / C^2), q1 and q2 are the charges, and d is the distance between them.
Force_1 = (8.99 * 10^9 N m^2 / C^2) * (1.5 * (10^-9 C) * 2.6 * (10^-9 C) ) / (0.65 m)^2
Calculating this, we get:
Force_1 = 0.62 N
Next, we can calculate the force between the charge at the origin and the charge at (0, 1.50 m) using Coulomb's Law:
Force_2 = (k * |q1 * q2|) / d^2
Force_2 = (8.99 * 10^9 N m^2 / C^2) * (1.5 * (10^-9 C) * 1.8 * (10^-9 C)) / (1.50 m)^2
Calculating this, we get:
Force_2 = 0.36 N
Since the charges are on the x and y-axes, the x-component of the net force is equal to the sum of the x-components of each individual force, and the y-component of the net force is equal to the sum of the y-components of each individual force.
Therefore, the x-component of the net force is 0.62 N and the y-component of the net force is -0.36 N.
Thus, the force acting on the charge at the origin is (0.62 N, -0.36 N).