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.

I don't know brother.

To find the magnitude of the net electric field at different points in space, we can combine the electric field due to the uniform electric field and the electric field due to the point charge.

The electric field due to the uniform electric field is easy to calculate. It has a constant magnitude and is directed in the positive x direction. We are given that the magnitude of the uniform electric field is 5700 N/C.

The electric field due to a point charge can be calculated using Coulomb's Law. Coulomb's Law states that the electric field due to a point charge is directly proportional to the charge and inversely proportional to the square of the distance from the charge.

(a) To find the magnitude of the net electric field at x = -0.13 m, we need to calculate the electric field due to the uniform electric field and the electric field due to 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 any point on the x-axis will have the same magnitude. Therefore, the electric field due to the uniform electric field at x = -0.13 m is also 5700 N/C.

2. Electric field due to the point charge:
To calculate the electric field due to the point charge at x = -0.13 m, we need to use Coulomb's Law. 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 Coulomb's constant (8.99 x 10^9 N*m^2/C^2)
q is the charge
r is the distance from the charge

Plugging in the values, we get:
E = (8.99 x 10^9 N*m^2/C^2) * (-5.4 x 10^-9 C) / (0.13 m)^2

Calculating this, we find the electric field due to the point charge at x = -0.13 m.

The net electric field at x = -0.13 m is the sum of the electric fields due to the uniform electric field and the point charge. To find the net electric field, we simply add the two electric fields together.

(b) Similarly, to find the magnitude of the net electric field at x = +0.13 m, we calculate the electric field due to the uniform electric field (5700 N/C) and the electric field due to the point charge using Coulomb's Law. Then we add these two electric fields together to find the net electric field.

(c) To find the magnitude of the net electric field at y = +0.13 m, we only need to consider the electric field due to the uniform electric field since the point charge does not have a component along the y-axis. Therefore, the magnitude of the net electric field at y = +0.13 m will be the same as the magnitude of the electric field due to the uniform electric field (5700 N/C).

By following this procedure, you can calculate the magnitude of the net electric field at each given point by combining the electric field due to the uniform electric field and the electric field due to the point charge using the appropriate formulas.