Two point charges are separated by 10.0 cm and have charges of 2.0 μC and -2 μC, respectively. What is the electric field at the point midway between the two charges? (k = 8.99 x 109 N.m2/C2)

A. 28.8 x 10 6
B. 14.4 x 106
C. 7.19 x 106
D. 3.59 x 106
E. zero

i am getting D...but i got that wrong i don't know how to solve it

To find the electric field at the point midway between two charges, you can calculate the electric field due to each charge individually and then add them together.

The formula to calculate 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 electrostatic constant (k = 8.99 x 10^9 N.m^2/C^2)
- Q is the charge of the point charge
- r is the distance from the point charge to the point where you want to calculate the electric field

Let's denote the electric field due to the positive charge (Q1) as E1, and the electric field due to the negative charge (Q2) as E2.

The charges are separated by a distance of 10.0 cm, so the distance from each charge to the point midway between them is 5.0 cm (half the distance).

First, calculate the electric field due to each charge:
E1 = k * (Q1 / r^2) = (8.99 x 10^9 N.m^2/C^2) * (2.0 x 10^-6 C) / (0.05 m)^2
E2 = k * (Q2 / r^2) = (8.99 x 10^9 N.m^2/C^2) * (-2.0 x 10^-6 C) / (0.05 m)^2

Now, add the electric fields together:
E_total = E1 + E2

Calculate the electric field at the point midway between the two charges using the given values and solve for E_total.

Now, let's calculate it:

E1 = (8.99 x 10^9 N.m^2/C^2) * (2.0 x 10^-6 C) / (0.05 m)^2
E1 = 2.87936 x 10^6 N/C

E2 = (8.99 x 10^9 N.m^2/C^2) * (-2.0 x 10^-6 C) / (0.05 m)^2
E2 = -2.87936 x 10^6 N/C

E_total = E1 + E2
E_total = 2.87936 x 10^6 N/C - 2.87936 x 10^6 N/C
E_total = 0 N/C

Therefore, the electric field at the point midway between the two charges is zero (option E).