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 = 0.120 m). The charges on the circle are -4.40 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°).

Question

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 = 0.120 m). The charges on the circle are -4.40 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°).

Answer 1

To calculate the net electrostatic force acting on the charge at the center of the compass, we need to find the individual forces exerted by the charges on the circle and then add them vectorially.

First, let's find the force exerted by the charge at the position due north on the center charge. The electrostatic force between two charges can be calculated using Coulomb's law:

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

Where:
F is the force between the charges,
k is the electrostatic constant (k = 9.0 x 10^9 N m^2/C^2),
|q1| and |q2| are the magnitudes of the charges,
r is the distance between the charges.

For the charge at the position due north:
|q1| = 4.40 µC = 4.40 x 10^-6 C
|q2| = 3.00 µC = 3.00 x 10^-6 C
r = 0.120 m

Using Coulomb's law, we can calculate the force exerted by the charge at the position due north:

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

Next, let's find the force exerted by the charge at the position due east on the center charge.

For the charge at the position due east:
|q1| = 5.00 µC = 5.00 x 10^-6 C
|q2| = 3.00 µC = 3.00 x 10^-6 C
r = 0.120 m

Using Coulomb's law, we can calculate the force exerted by the charge at the position due east:

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

Now, we have the force exerted by the charge at the position due north (Fnorth) and the force exerted by the charge at the position due east (Feast). To calculate the net force, we need to add these two forces vectorially.

Since the forces are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the net force:

|Fnet| = sqrt(Fnorth^2 + Feast^2)

To find the direction of the net force, we can use trigonometry. Let's call the angle between the net force and the position due east θ. We can use the inverse tangent function to calculate this angle:

θ = atan(Fnorth / Feast)

With these calculations, we can find the magnitude and direction of the net electrostatic force acting on the charge at the center.