A charge of -3.17 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 -3.96 μC at the position due north and +5.03 μC at the position due east. What is the magnitude of the net electrostatic force acting on the charge at the center?

Question

A charge of -3.17 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 -3.96 μC at the position due north and +5.03 μC at the position due east. What is the magnitude of the net electrostatic force acting on the charge at the center?

Answer 1

F = k Q1Q2/r^2

here r = .115 so let (k/r^2) = c constant

Fnorth = -(3.17*3.96*10^-12)c

Feast = +(3.17*5.03*10^-12)c

magnitude = sqrt (Fx^2 + Fy ^2)

Answer 2

To find the magnitude of the net electrostatic force acting on the charge at the center, we need to calculate the individual forces due to each of the charges on the circle and then find their vector sum.

First, let's calculate the force due to the charge at the position due north. The formula to calculate the electrostatic force between two charges is given by Coulomb's Law:

F = k * (|q1| * |q2|) / r^2

Where:
F is the electrostatic force
k is the electrostatic constant (k = 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

In this case, |q1| (charge at the center) = |q3| = 3.17 μC = 3.17 x 10^-6 C
|q2| (charge due north) = 3.96 μC = 3.96 x 10^-6 C
r = radius of the compass = 0.115 m

Using the formula, we can calculate the force due to the charge at the position due north:

F1 = k * (|q1| * |q2|) / r^2
= (8.99 x 10^9 N m^2/C^2) * (3.17 x 10^-6 C) * (3.96 x 10^-6 C) / (0.115 m)^2

Now, let's calculate the force due to the charge at the position due east. The steps are similar to the previous calculation:

|q2| (charge due east) = 5.03 μC = 5.03 x 10^-6 C

F2 = k * (|q1| * |q2|) / r^2
= (8.99 x 10^9 N m^2/C^2) * (3.17 x 10^-6 C) * (5.03 x 10^-6 C) / (0.115 m)^2

Finally, we can find the magnitude of the net electrostatic force acting on the charge at the center by adding the magnitudes of F1 and F2:

|F_net| = |F1| + |F2|

Thus, by calculating the individual forces and then finding their vector sum, you can determine the magnitude of the net electrostatic force acting on the charge at the center.