A charge of -3.95C 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 -5.90C at the position due north and +4.27C at the position due east. What is (a) the magnitude and (b) direction of the net electrostatic force acting on the charge at the center? Specify the direction as an angle relative to due east.

Question

A charge of -3.95C 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 -5.90C at the position due north and +4.27C at the position due east. What is (a) the magnitude and (b) direction of the net electrostatic force acting on the charge at the center? Specify the direction as an angle relative to due east.

Answer 1

To find the net electrostatic force acting on the charge at the center, we need to consider the individual forces acting on the charge due to the other two charges.

(a) To find the magnitude of the net electrostatic force, we can use Coulomb's Law, which states that the force between two charges is 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: The electrostatic force between the two charges
k: Coulomb's constant (k ≈ 8.99 x 10^9 Nm^2/C^2)
|q1|, |q2|: The magnitudes of the charges
r: The distance between the charges

First, let's find the force between the charges at the position due north and the charge at the center:
|q1| = 5.90C, |q2| = 3.95C (opposite signs, since they have different charges)
r = radius of the circle = 0.135m

Using the formula, we have:
F1 = k * (|q1| * |q2|) / r^2
F1 = (8.99 x 10^9 Nm^2/C^2) * (5.90C * 3.95C) / (0.135m)^2

Next, let's find the force between the charge at the position due east and the charge at the center:
|q1| = 4.27C, |q2| = 3.95C (same sign, since they have the same charge)
r = radius of the circle = 0.135m

Using the formula, we have:
F2 = k * (|q1| * |q2|) / r^2
F2 = (8.99 x 10^9 Nm^2/C^2) * (4.27C * 3.95C) / (0.135m)^2

Now, we can find the net electrostatic force by summing the two forces:
F_net = √(F1^2 + F2^2)

(b) To find the direction of the net electrostatic force, we can use the inverse tangent (arctan) function to determine the angle relative to due east.

Let's find the angle using the formula:
θ = arctan(F2/F1)

Now, let's substitute the values into the equations to find the magnitude and direction of the net electrostatic force acting on the charge at the center.