Three point charge of 2NC 7NC and - 4NC are located at the corners of an equilateral triangl as shown below. Caculate the magnitude and direction of the net force on the 7uc charge.
To calculate the magnitude and direction of the net force on the 7uC charge, we need to consider the interaction between the charges.
Let's label the charges as follows:
- Charge A: 2 uC (located at one corner of the triangle)
- Charge B: 7 uC (located at another corner of the triangle)
- Charge C: -4 uC (located at the remaining corner of the triangle)
First, let's calculate the distance between the charges. Since the triangle is equilateral, all sides are equal. Let's denote this distance by 'd'.
Next, let's calculate the magnitudes of the individual forces on the 7 uC charge due to the other two charges.
1. Force between the 7 uC and 2 uC charges:
The equation to calculate the force between two charges is given by Coulomb's Law:
Force_AB = (k * |q1 * q2|) / r^2
where:
- k is the electrostatic constant (k = 9 * 10^9 N * m^2 / C^2)
- q1 is the magnitude of charge A (2 uC)
- q2 is the magnitude of charge B (7 uC)
- r is the distance between the charges (d)
2. Force between the 7 uC and -4 uC charges:
Similarly, we need to calculate the force between these two charges using Coulomb's Law:
Force_BC = (k * |q1 * q2|) / r^2
where:
- q1 is the magnitude of charge B (7 uC)
- q2 is the magnitude of charge C (-4 uC)
- r is again the distance between the charges (d)
Now, let's determine the direction of the net force. We need to consider the vector nature of the forces. Since the 2 uC charge and the -4 uC charge have opposite signs, their forces will act in opposite directions on the 7 uC charge. The net force will be the vector sum of these two forces.
Once we have calculated the magnitudes and direction of the two individual forces, we can add them as vectors to obtain the net force on the 7 uC charge. That will give us the final magnitude and direction of the net force.
Note: To calculate a more accurate value, we would need to know the distance between the charges, which is missing in your question.