Two point charges, one of +3.00 10-5 C and the other -5.00 10-5 C are placed at adjacent corners of a square 1.400 m on a side. A third charge of +5.70 10-5 C is placed at the corner diagonally opposite to the negative charge. Calculate the magnitude and direction of the force acting on the third charge. For the direction, determine the angle the force makes relative to a line joining the first two charges.
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To calculate the magnitude and direction of the force acting on the third charge, we can use Coulomb's law. Coulomb's law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = (k * |q1 * q2|) / r^2
Where:
F is the magnitude of the force
k is the electrostatic constant
q1 and q2 are the charges of the two objects
r is the distance between the two objects
Let's calculate the magnitude of the force first:
Given:
Charge of the first object (q1) = +3.00 * 10^-5 C
Charge of the second object (q2) = -5.00 * 10^-5 C
Charge of the third object = +5.70 * 10^-5 C
Distance between the first two charges (r) = 1.400 m
Plugging in the values into the formula:
F = [(9 * 10^9 Nm^2/C^2) * |(+3.00 * 10^-5 C) * (-5.00 * 10^-5 C)|] / (1.400 m)^2
Calculating the magnitude of the force:
F = [(9 * 10^9 Nm^2/C^2) * (1.50 * 10^-9 C^2)] / 1.96 m^2
= 10.23 N (approximately)
Now let's calculate the direction of the force. The force acting on the third charge is directed toward the positive charge and away from the negative charge. To find the angle the force makes relative to a line joining the first two charges, we can use the concept of trigonometry.
Let's call the angle between the force and the line joining the charges as theta (θ).
tan(θ) = opposite/adjacent
In this case, the opposite side is the vertical distance between the charges, which is equal to the side length of the square (1.400 m), and the adjacent side is the horizontal distance between the charges, also equal to the side length of the square (1.400 m).
tan(θ) = 1.400 m / 1.400 m
tan(θ) = 1
Taking the inverse tangent (arctan) of both sides:
θ = arctan(1)
θ = 45 degrees
Therefore, the magnitude of the force is 10.23 N, and the angle it makes relative to the line joining the charges is 45 degrees.