A positive and a negative charge are positioned as shown:
+
|
|_______ -
The distance from - to corner is 4.00m and the distance from corner to + is 3.00m.
Q1 = 4.00 microCoulomb
Q2 = -4.00 microCoulomb
1. What is the distance between the charges?
2. What is the angle of West of south?
3. What is the force of + on -?
4. What is the force of - on +?
To find the answers to these questions, we can use the concepts of Coulomb's law and trigonometry. Let's break down each question step by step:
1. What is the distance between the charges?
To find the distance between the charges, you need to use the Pythagorean theorem since the two distances given form a right triangle. The horizontal distance between the charges is 4.00m, and the vertical distance is 3.00m. Using the Pythagorean theorem, the formula is:
distance = √(horizontal distance^2 + vertical distance^2)
Plugging in the numbers, you get:
distance = √(4.00m^2 + 3.00m^2)
distance = √(16.00m^2 + 9.00m^2)
distance = √(25.00m^2)
distance = 5.00m
Therefore, the distance between the charges is 5.00m.
2. What is the angle of West of south?
To find the angle, you can use trigonometric functions. Since the triangle is a right triangle, you can use the tangent function to find the angle. The angle you want is the angle between the vertical (South) and the diagonal. The formula is:
angle = tan^(-1)(vertical distance / horizontal distance)
Plugging in the numbers, you get:
angle = tan^(-1)(3.00m / 4.00m)
angle ≈ 36.87°
Therefore, the angle West of South is approximately 36.87°.
3. What is the force of + on -?
To find the force between the charges, you can use Coulomb's law. The formula is:
force = (k * |Q1 * Q2|) / distance^2
k is the electrostatic constant, which is approximately 9.0 x 10^9 N*m^2/C^2, Q1 is the magnitude of the first charge (4.00 μC), Q2 is the magnitude of the second charge (-4.00 μC), and distance is the distance between the charges (5.00m).
Plugging in the numbers, you get:
force = (9.0 x 10^9 N*m^2/C^2 * |4.00 μC * -4.00 μC|) / (5.00m)^2
force = (9.0 x 10^9 N*m^2/C^2 * 4.00 μC * 4.00 μC) / 25.00m^2
force = (9.0 x 10^9 N*m^2/C^2 * 16.00 μC^2) / 25.00m^2
force = 5.76 x 10^-2 N
Therefore, the force of the positive charge on the negative charge is approximately 5.76 x 10^-2 N.
4. What is the force of - on +?
Since the charges have equal magnitude but opposite signs, the force between them will be the same as in question 3, but with opposite direction. Therefore, the force of the negative charge on the positive charge will be approximately -5.76 x 10^-2 N, indicating an attractive force.
Note: It's important to use the absolute value of the charges when calculating the force, as the force between charges is determined by their magnitudes, not their signs.