Background pertinent to this problem is available in Interactive LearningWare 18.3. A uniform electric field exists everywhere in the x, y plane. This electric field has a magnitude of 5700 N/C and is directed in the positive x direction. A point charge -5.4 × 10-9 C is placed at the origin. Find the magnitude of the net electric field at (a) x = -0.13 m, (b) x = +0.13 m, and (c) y = +0.13 m.

To find the magnitude of the net electric field at different points in the x-y plane, we need to calculate the electric field due to the uniform electric field and the electric field due to the point charge at each point. Then, we can add these two electric fields vectorially to get the net electric field.

Let's start with point (a) where x = -0.13 m. To find the net electric field at this point, we need to find the individual electric fields due to the uniform electric field and the point charge.

1. Electric field due to the uniform electric field:
Since the uniform electric field is directed only in the positive x direction, the electric field at point (a) due to the uniform electric field will be zero.

2. Electric field due to the point charge:
The electric field due to a point charge can be calculated using Coulomb's Law:

E = k * (Q / r^2)

Where:
- E is the electric field
- k is the electrostatic constant (9 × 10^9 N m^2/C^2)
- Q is the magnitude of the point charge (-5.4 × 10^-9 C)
- r is the distance from the point charge to the point where the electric field is being calculated

At point (a), the distance from the origin (where the point charge is located) is 0.13 m. Plugging in these values, we can calculate the electric field due to the point charge at point (a).

3. Calculating the net electric field:
To find the net electric field, we need to add the electric field due to the uniform electric field and the electric field due to the point charge vectorially. Since the electric field due to the uniform electric field is zero at point (a), the net electric field will be equal to the electric field due to the point charge.

Repeat the above steps for points (b) and (c) where x = +0.13 m and y = +0.13 m, respectively, to find the net electric field at those points.

Note: In this problem, since the electric field due to the uniform electric field does not contribute to the net electric field at points (a), (b), and (c), the net electric field at those points will be solely due to the point charge.