A positive and a negative charge are positioned as shown:
+
| 3.00 meters
- _______|
4.00 meters
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 answer these questions, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The equation for Coulomb's Law is:
F = k * (|Q1| * |Q2|) / r^2
Where:
- F is the magnitude of the electrostatic force
- k is Coulomb's constant (8.99 x 10^9 N*m^2/C^2)
- Q1 and Q2 are the magnitudes of the charges
- r is the distance between the charges
Let's calculate the answers using this information:
1. What is the distance between the charges?
The distance between the charges is given as 3.00 meters in the horizontal direction and 4.00 meters in the vertical direction. We can use the Pythagorean theorem to find the distance, d:
d = √(3.00^2 + 4.00^2)
= √(9 + 16)
= √25
= 5.00 meters
Therefore, the distance between the charges is 5.00 meters.
2. What is the angle of West of south?
To determine the angle, you need to find the tangent of the angle:
tan(theta) = opposite/adjacent
tan(theta) = 4.00/3.00
theta = tan^(-1)(4.00/3.00)
Using a calculator, the angle of West of south is approximately 53.13 degrees.
3. What is the force of + on -?
To find the force of the positive charge on the negative charge, we'll substitute the given values into Coulomb's Law equation:
F = k * (|Q1| * |Q2|) / r^2
F = (8.99 x 10^9 N*m^2/C^2) * [(4.00 x 10^(-6) C) * (4.00 x 10^(-6) C)] / (5.00 m)^2
Simplifying:
F = (8.99 x 10^9 N*m^2/C^2) * (16.00 x 10^(-12) C^2) / (25.00 m^2)
F ≈ 5.76 x 10^(-2) N
Therefore, the force of the positive charge on the negative charge is approximately 5.76 x 10^(-2) Newton.
4. What is the force of - on +?
The magnitude of the force between the two charges does not change, only the direction. Since the charges are equal in magnitude, the force of the negative charge on the positive charge will have the same magnitude but the opposite direction.
Therefore, the force of the negative charge on the positive charge is approximately 5.76 x 10^(-2) Newton, but in the opposite direction.