# 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

_________°

For Further Reading

Physics - Bobpursley, Thursday, August 30, 2007 at 1:52am

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

## Use Coulombs' Law:

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

***(q1 and q2 are the absolute values--so the sign is positive even if the given value is negative)

***K is the constant: 8.99 x 10^9N*m^2/C^2

***r is the radius

The question wants you to find the net force acting on the center particle--so Fnet= Force on center by the particle due east + the force on the center by the particle due north

Use Coulomb's Law to find the individual forces that the particles exert: (change uC to C for the equation)

Force on center by East= 8.99x10^9 (3.0x10^-6)(5.0x10^-6)/(0.135)^2

***There is no Y component for this force

*** The center charge is - and the east charge is + so the particles attract and the east charge has a force in the negative direction

Force on center by North: 8.99x10^9 (3.0x10^-6)(3.20x10^-6)/ (0.135)^2

***There is no X component for this force

***Like charges repel, so the force will be away from the center in the positive y direction.

Now, use A^2+B^2=C^2 to solve for C (this will be the vector sum of the forces) A=Force on center by North and B=Force on center by East (The answers you obtain from the two previous equations)

C will be your answer. (I don't have a calculator)

Direction: tan^-1 (opposite or y vector/adjacent or x vector)

## To find the magnitude and direction of the net electrostatic force acting on the charge at the center of the compass, you will need to calculate the forces exerted by the two charges on the circle and then add them as vectors.

Step 1: Calculate the force due to the charge at the North position.

Using Coulomb's law, the magnitude of the force (FN) between the two charges is given by:

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

where k is the electrostatic constant (9.0 × 10^9 N m^2/C^2), q1 is the charge at the center (-3.00 µC), q2 is the charge at the North position (-3.20 µC), and r is the radius of the circle (0.135 m).

FN = (9.0 × 10^9 N m^2/C^2) * (-3.00 × 10^-6 C) * (-3.20 × 10^-6 C) / (0.135 m)^2

Step 2: Calculate the force due to the charge at the East position.

Using the same formula, the magnitude of the force (FE) between the two charges is given by:

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

where q2 is the charge at the East position (+5.00 µC).

FE = (9.0 × 10^9 N m^2/C^2) * (-3.00 × 10^-6 C) * (5.00 × 10^-6 C) / (0.135 m)^2

Step 3: Add the forces as vectors.

To add the forces as vectors, you need to decompose them into their x and y components. The North force (FN) only has a y-component, while the East force (FE) only has an x-component.

Since these forces are at right angles to each other, you can find the net force (F) by using the Pythagorean theorem:

F = √(FN^2 + FE^2)

The direction of the net force with respect to due east (0°) can be found using the inverse tangent function:

θ = arctan(FE / FN)

Calculate FN and FE using the given values and plug them into the above equations to find the magnitude (F) and direction (θ) of the net electrostatic force acting on the charge at the center.

## To find the magnitude and direction of the net electrostatic force acting on the charge at the center of the compass, we can follow these steps:

1. Calculate the force between the center charge and the charge at the north position:

- Use Coulomb's Law to calculate the force between two charges: F = (k * |q1| * |q2|) / r^2.

- Where F is the force, k is the electrostatic constant (9 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between them.

- In this case, the center charge is -3.00 µC, and the north charge is -3.20 µC.

- The distance between them is the radius of the compass, which is 0.135 m.

- Calculate the force F_S (force from center to north): F_S = (k * |-3.00 µC| * |-3.20 µC|) / (0.135 m)^2.

2. Calculate the force between the center charge and the charge at the east position:

- Use the same formula as above, but now the charges are -3.00 µC and +5.00 µC (opposite signs).

- Calculate the force F_E (force from center to east): F_E = (k * |-3.00 µC| * |5.00 µC|) / (0.135 m)^2.

3. Use vector addition to find the net force:

- Treat the forces F_S and F_E as vectors.

- The net force, F_net, is the vector sum of F_S and F_E.

- To calculate the net force vector, add the magnitudes of the forces and consider their directions.

4. Calculate the magnitude of the net force:

- Use the Pythagorean theorem: F_net = sqrt(F_S^2 + F_E^2).

- Substitute the values of F_S and F_E calculated earlier.

5. Calculate the direction of the net force:

- Use trigonometry to find the angle θ between the net force and the due east direction.

- The tangent of θ is given by the ratio of F_E to F_S: tan(θ) = F_E / F_S.

- Use the inverse tangent function to find the angle: θ = atan(F_E / F_S).

- Convert the angle from radians to degrees.

By following these steps, you should be able to find the magnitude and direction of the net electrostatic force acting on the charge at the center of the compass.