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 = 0.115 m). The charges on the circle are -4.70 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
To find the magnitude of the net electrostatic force acting on the charge at the center, we can use Coulomb's Law which states that the force between two 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:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the electrostatic force
k is the electrostatic constant, approximately equal to 9 x 10^9 N * m^2 / C^2
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
In this case, the charge at the center has a magnitude of -3.00 µC, the charge at the north position has a magnitude of -4.70 µC, and the charge at the east position has a magnitude of +5.00 µC. The distance between the charges is the radius of the circle, which is 0.115 m.
First, we need to calculate the force between the charge at the center and the charge at the north position.
F_north = k * (|-3.00 µC| * |-4.70 µC|) / (0.115 m)^2
Next, we calculate the force between the charge at the center and the charge at the east position.
F_east = k * (|-3.00 µC| * |5.00 µC|) / (0.115 m)^2
Finally, we find the net electrostatic force acting on the charge at the center by summing the forces from both positions. Since the force at the north position acts towards the center of the circle and the force at the east position acts away from the center, we need to subtract the force at the east position from the force at the north position.
Net force = F_north - F_east
Plug in the values into the formulas, perform the calculations, and you will find the magnitude of the net electrostatic force acting on the charge at the center.