four charged particles are placed so that each particle is at the corner of a square. the sides of the square are 15 cm. the charge at the upper left corner is +3.0 microcoulombs, the charge at the upper right corner is -6.0 microcoulombs, the charge at the lower left corner is -2.4 microcoulombs, and the charge at the lower right corner is -9.0 microcoulombs. what is the net electric force on the +3.0 micro coulombs charge? what is the net electric force on the -6.0 microcoulombs charge? What is the net electric froe on the -9.0 microcoulombs charge?.
To calculate the net electric force on each charge, we need to consider the forces exerted by the other charges. The net electric force is the vector sum of these individual forces.
The electric force between two charges can be calculated using Coulomb's law:
F = k * (q1 * q2) / r^2
Where:
- F is the electric force between the charges,
- k is the electrostatic constant (k = 9 x 10^9 N*m^2/C^2),
- q1 and q2 are the magnitudes of the charges, and
- r is the distance between the charges.
Let's calculate the net electric force on each charge step-by-step:
1. Net electric force on the +3.0 microcoulombs charge:
- Calculate the force from the -6.0 microcoulombs charge:
F1 = k * ((3.0 x 10^-6 C) * (-6.0 x 10^-6 C)) / (15 cm)^2
- Calculate the force from the -2.4 microcoulombs charge:
F2 = k * ((3.0 x 10^-6 C) * (-2.4 x 10^-6 C)) / (15 cm)^2
- Calculate the force from the -9.0 microcoulombs charge:
F3 = k * ((3.0 x 10^-6 C) * (-9.0 x 10^-6 C)) / (15 cm)^2
- Calculate the net electric force:
Net force = F1 + F2 + F3
2. Net electric force on the -6.0 microcoulombs charge:
- Calculate the force from the +3.0 microcoulombs charge:
F4 = k * ((-6.0 x 10^-6 C) * (3.0 x 10^-6 C)) / (15 cm)^2
- Calculate the force from the -2.4 microcoulombs charge:
F5 = k * ((-6.0 x 10^-6 C) * (-2.4 x 10^-6 C)) / (15 cm)^2
- Calculate the force from the -9.0 microcoulombs charge:
F6 = k * ((-6.0 x 10^-6 C) * (-9.0 x 10^-6 C)) / (15 cm)^2
- Calculate the net electric force:
Net force = F4 + F5 + F6
3. Net electric force on the -9.0 microcoulombs charge:
- Calculate the force from the +3.0 microcoulombs charge:
F7 = k * ((-9.0 x 10^-6 C) * (3.0 x 10^-6 C)) / (15 cm)^2
- Calculate the force from the -6.0 microcoulombs charge:
F8 = k * ((-9.0 x 10^-6 C) * (-6.0 x 10^-6 C)) / (15 cm)^2
- Calculate the force from the -2.4 microcoulombs charge:
F9 = k * ((-9.0 x 10^-6 C) * (-2.4 x 10^-6 C)) / (15 cm)^2
- Calculate the net electric force:
Net force = F7 + F8 + F9
By following these calculations for each charge, you can find the net electric force on each charge.
To find the net electric force on each charge, you need to calculate the electric force between each pair of charges and sum them up vectorially.
The electric force between two charged particles can be calculated using Coulomb's law:
F = (k * |q1 * q2|) / r^2
Where:
- F is the electric force between the charges (in Newtons)
- k is the Coulomb's constant, approximately equal to 9 × 10^9 Nm²/C²
- q1 and q2 are the magnitudes of the charges (in Coulombs)
- r is the distance between the charges (in meters)
To apply Coulomb's law between two charges, you need to choose one charge and calculate the force exerted by the other charges on it. Repeat this process for each charge, and then sum up the forces vectorially.
Let's start by calculating the net electric force on the +3.0 microcoulombs charge:
1. Calculate the force exerted by the -6.0 microcoulombs charge on the +3.0 microcoulombs charge:
F1 = (k * |q1 * q2|) / r^2
F1 = (9 × 10^9 * |3.0 × 10^-6 * -6.0 × 10^-6|) / (15 × 10^-2)^2
2. Calculate the force exerted by the -2.4 microcoulombs charge on the +3.0 microcoulombs charge:
F2 = (k * |q1 * q2|) / r^2
F2 = (9 × 10^9 * |3.0 × 10^-6 * -2.4 × 10^-6|) / (15 × 10^-2)^2
3. Calculate the force exerted by the -9.0 microcoulombs charge on the +3.0 microcoulombs charge:
F3 = (k * |q1 * q2|) / r^2
F3 = (9 × 10^9 * |3.0 × 10^-6 * -9.0 × 10^-6|) / (15 × 10^-2)^2
4. Calculate the net force on the +3.0 microcoulombs charge by summing up the forces vectorially:
Net Force = √((F1 * cos θ1 + F2 * cos θ2 + F3 * cos θ3)^2 + (F1 * sin θ1 + F2 * sin θ2 + F3 * sin θ3)^2)
Here, cos θ and sin θ represent the angles between the forces and the x-axis or y-axis, respectively.
Repeat the above steps for the -6.0 microcoulombs and -9.0 microcoulombs charges to find their net electric forces.
It's important to convert the charges from microcoulombs to Coulombs and the distance from centimeters to meters in the calculations. Make sure to use the correct signs in the force calculations, as the charges are both positive and negative.