A charge of -3.00 µC is fixed at the center of a compass. Two additional charges are fixed on the circle of the compass (radius = 0.135 m). The charges on the circle are -3.20 µC at the position due north and +5.00 µC at the position due east. What is the magnitude and direction of the net electrostatic force acting on the charge at the center? Specify the direction relative to due east (0°).
Magnitude
_________N
Direction
_________°
assume the charges don't move. Work this as a vector problem. Find the force S due to the center charge and the N charge, and the Force E due to the center charge and the E charge. Add those as vectors
To find the magnitude and direction of the net electrostatic force acting on the charge at the center, we can use Coulomb's Law.
Coulomb's Law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is given as:
F = k * (|q1 * q2| / r^2)
Where:
- F is the magnitude of the electrostatic force
- k is the electrostatic constant, approximately equal to 9 * 10^9 Nm^2/C^2
- q1 and q2 are the magnitudes of the two charges
- r is the distance between the charges
Let's calculate the net electrostatic force on the charge at the center.
First, we need to calculate the distance between the charge at the center and the charges on the circle. Since the charge at the center is fixed, the distance between the center and any point on the circle will be the same, equal to the radius of the compass: 0.135 m.
Now, let's calculate the force between the -3.00 µC charge at the center and the -3.20 µC charge on the circle.
F1 = k * (|-3.00 µC * -3.20 µC| / (0.135 m)^2)
Next, let's calculate the force between the -3.00 µC charge at the center and the +5.00 µC charge on the circle.
F2 = k * (|-3.00 µC * +5.00 µC| / (0.135 m)^2)
Finally, the net electrostatic force can be calculated by taking the vector sum of the two forces:
Net F = √(F1^2 + F2^2)
After calculating these values, we will have the magnitude of the net electrostatic force. To find the direction, we can use trigonometry.
The angle, θ, can be calculated using the tangent function:
θ = arctan(F2/F1)
This angle represents the direction of the force relative to due east (0°).