A 2 μC charge is placed at × = 1 m while a second 2 μC Charge is placed at x=-1. Find (a) the electric field at y = 0.5 m, and (b) the electric force a -3 μC charge placed at y=0.5 m.

To find the electric field at a specific point due to multiple charges, we can use the principle of superposition. The total electric field at any point is the vector sum of the electric fields created by each charge individually.

(a) To find the electric field at y = 0.5 m, we need to calculate the electric field created by each charge at that point and then add them together.

Step 1: Calculate the electric field created by the 2 μC charge at x = 1 m.
The formula for the electric field due to a point charge is given by:
E = k * Q / r^2

Where:
E is the electric field
k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2)
Q is the charge of the source
r is the distance between the point charge and the location where we want to find the field.

In this case, the charge of the source (Q) is 2 μC = 2 x 10^-6 C, and the distance (r) is the horizontal distance from the charge to the point of interest. Since the charge is placed at x = 1 m, the distance is r = 1 m - 0 m = 1 m.

Substituting these values into the formula:
E1 = (8.99 x 10^9 N m^2/C^2) * (2 x 10^-6 C) / (1 m)^2

Step 2: Calculate the electric field created by the 2 μC charge at x = -1 m.
Following the same steps as above, the distance (r) is the horizontal distance from the charge to the point of interest. Since the charge is placed at x = -1 m, the distance is r = 0 m - (-1 m) = 1 m.

Substituting the values into the formula:
E2 = (8.99 x 10^9 N m^2/C^2) * (2 x 10^-6 C) / (1 m)^2

Step 3: Add the individual electric fields to get the total electric field.
E_total = E1 + E2

(b) To find the electric force on a -3 μC charge placed at y = 0.5 m, we can use the formula for the electric force between two charges.

Step 1: Calculate the electric force between the -3 μC charge and each of the 2 μC charges.
The formula for electric force between two charges is given by:
F = k * (|Q1| * |Q2|) / r^2

Where:
F is the electric force
k is the Coulomb's constant (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 two charges.

In this case, one charge is -3 μC = -3 x 10^-6 C, and the distance (r) is the vertical distance from the charge to the point of interest. Since the charge is placed at y = 0.5 m, the distance is r = 0.5 m - 0 m = 0.5 m.

Substituting these values into the formula:
F1 = (8.99 x 10^9 N m^2/C^2) * (|-3 x 10^-6 C| * |2 x 10^-6 C|) / (0.5 m)^2

Step 2: Calculate the electric force between the -3 μC charge and the other 2 μC charge using the same steps.
F2 = (8.99 x 10^9 N m^2/C^2) * (|-3 x 10^-6 C| * |2 x 10^-6 C|) / (0.5 m)^2

Step 3: Add up the individual electric forces to get the total electric force.
F_total = F1 + F2

By following these steps, you should be able to find the values of the electric field and electric force at the given points.