Three charges, +2.5 µC, -4.3 µC, and -6.0 µC, are located at (-0.20 m, 0.15 m), (0.50 m, -0.35 m), and (-0.42 m, -0.32 m), respectively. What is the electric field at the origin?

Ma’am

To find the electric field at the origin, we need to calculate the contribution of each charge to the electric field and then sum them up. The electric field at a point due to a point charge is given by Coulomb's law:

E = k * (Q / r^2)

where E is the electric field, k is the electrostatic constant (8.99 x 10^9 N m^2/C^2), Q is the charge, and r is the distance from the charge to the point where we want to find the electric field.

Let's calculate the electric field due to each charge and then add them up:

Charge 1: +2.5 µC at (-0.20 m, 0.15 m)
The distance from the charge to the origin is:
r1 = sqrt((-0.20 m)^2 + (0.15 m)^2)

Now, we can calculate the electric field due to this charge:
E1 = k * (Q1 / r1^2)

Charge 2: -4.3 µC at (0.50 m, -0.35 m)
The distance from the charge to the origin is:
r2 = sqrt((0.50 m)^2 + (-0.35 m)^2)

Now, we can calculate the electric field due to this charge:
E2 = k * (Q2 / r2^2)

Charge 3: -6.0 µC at (-0.42 m, -0.32 m)
The distance from the charge to the origin is:
r3 = sqrt((-0.42 m)^2 + (-0.32 m)^2)

Now, we can calculate the electric field due to this charge:
E3 = k * (Q3 / r3^2)

Finally, we can add up the individual electric fields:
E = E1 + E2 + E3

Substituting the values for each charge and calculating the electric field will give us the answer.