the positive point charges + q are placed at three corners of a square , and a negative point charge -Q is placed at the fourth , corner. the side of the square is L. calculate the net electric force that positive charges exert on the negative charge
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To calculate the net electric force that the positive charges exert on the negative charge in this scenario, we can use the principle of superposition, which states that the net force experienced by a charge due to multiple charges is the vector sum of the individual forces.
In this case, let's assume that the positive charges +q are located at three corners of the square, and the negative charge -Q is placed at the fourth corner. Since all the charges are point charges, we can apply Coulomb's law to determine the force between each pair of charges.
Coulomb's law states that the electric force between two point 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 electric force between two 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
- r is the distance between the charges
Now, we can calculate the net force experienced by the negative charge due to the positive charges at each corner, and then find the resultant force.
Let's assume the side length of the square is L:
1. Calculate the force between the negative charge -Q and each positive charge +q:
F1 = (k * |-Q * q|) / L^2
F2 = (k * |-Q * q|) / L^2
F3 = (k * |-Q * q|) / L^2
2. As the charges are arranged symmetrically, the direction of forces F1, F2, and F3 are along the diagonals of the square, pointing towards the center.
3. To find the net force, we need to calculate the vector sum of the forces:
Net Force = F1 + F2 + F3
Since the forces are all in the same direction, we don't need to consider different components. Just add up the magnitudes of the forces.
Finally, you can substitute the appropriate values into the equation and solve for the net electric force on the negative charge.