2. 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 = 0.1 m). The charges on the circle are -4.0 µC at the position due north and +5.0 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.
Just how is anyone going to guess what the School Subject is with "umt?" Please look in the red margin to the left, up high, to pick a school subject someone might recognize. I only read your post out of curiosity but a teacher of the subject WILL read it, if the School Subject is recognizable.
Sra
To find the magnitude and direction of the net electrostatic force acting on the charge at the center, we can use Coulomb's law and vector addition.
Coulomb's law states that the electrostatic force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, it can be written as:
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 problem, the charge at the center has a magnitude of -3.00 µC, and the two charges on the circle have magnitudes of -4.0 µC and +5.0 µC. The radius of the circle is given as 0.1 m.
First, let's find the net electrostatic force due to the charge at the position due north. The distance between the center charge and the north charge is the radius of the circle, 0.1 m. Plugging the values into Coulomb's law:
F_north = k * |-3.00 µC| * |-4.0 µC| / (0.1 m)^2
Next, let's find the net electrostatic force due to the charge at the position due east. The distance between the center charge and the east charge is also the radius of the circle, 0.1 m. Plugging the values into Coulomb's law:
F_east = k * |-3.00 µC| * |+5.0 µC| / (0.1 m)^2
Now, to find the net electrostatic force acting on the charge at the center, we need to combine the forces due to the north and east charges using vector addition. Since both forces act at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the net force:
F_net = √(F_north^2 + F_east^2)
To determine the direction of the net force relative to due east, we can use trigonometry and the inverse tangent (tan^(-1)) function:
θ = tan^(-1)(F_north / F_east)
The angle θ will indicate the direction of the net electrostatic force clockwise from due east.
By substituting the values into the above equations, you can calculate the magnitude and direction of the net electrostatic force acting on the charge at the center.