Three charges, +2.5 micro coulomb, -4 micro coulomb and 6.3 micro coulomb, are located at (0.20m, .15m), (.50m, -.35m), and (-.42m,-.32m) respectively. What is the electric field at the origin?

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To find the electric field at the origin, we can use the principle of superposition. The principle states that the electric field created by multiple charges is the vector sum of the individual electric fields created by each charge.

Given the three charges and their positions, we can calculate the electric field at the origin as follows:

1. Calculate the electric field created by the first charge:
- The first charge has a magnitude of +2.5 micro coulomb and is located at (0.20m, 0.15m).
- The distance, r1, between the first charge and the origin is given by:
r1 = √(x1^2 + y1^2) = √((0.20m)^2 + (0.15m)^2)
- The electric field, E1, created by the first charge is given by Coulomb's law:
E1 = k * Q1 / r1^2, where
- k = 9 * 10^9 Nm^2/C^2 (Coulomb's constant)
- Q1 = +2.5 * 10^-6 C (charge of the first charge)

2. Calculate the electric field created by the second charge:
- The second charge has a magnitude of -4 micro coulomb and is located at (0.50m, -0.35m).
- The distance, r2, between the second charge and the origin is given by:
r2 = √(x2^2 + y2^2) = √((0.50m)^2 + (-0.35m)^2)
- The electric field, E2, created by the second charge is given by Coulomb's law:
E2 = k * Q2 / r2^2, where
- Q2 = -4 * 10^-6 C (charge of the second charge)

3. Calculate the electric field created by the third charge:
- The third charge has a magnitude of 6.3 micro coulomb and is located at (-0.42m, -0.32m).
- The distance, r3, between the third charge and the origin is given by:
r3 = √(x3^2 + y3^2) = √((-0.42m)^2 + (-0.32m)^2)
- The electric field, E3, created by the third charge is given by Coulomb's law:
E3 = k * Q3 / r3^2, where
- Q3 = 6.3 * 10^-6 C (charge of the third charge)

4. Finally, calculate the total electric field at the origin by adding the electric fields created by each charge vectorially:
E_total = E1 + E2 + E3

Substitute the values and calculate the electric field at the origin.