The electric field midway between two equal but opposite point charges is 825 N/C, and the distance between the charges is 9 cm. What is the magnitude of the charge on each?

To find the magnitude of the charge on each point charge, we can use the formula for the electric field between two point charges:

E = k * q / r^2

Where:
- E is the electric field
- k is the Coulomb's constant (approximately 9 x 10^9 N m^2/C^2)
- q is the magnitude of the charge
- r is the distance between the charges

In this case, we are given the electric field E = 825 N/C and the distance r = 9 cm = 0.09 m. We need to solve for q.

Rearranging the formula, we have:

q = E * r^2 / k

Let's substitute the values into the formula:

q = (825 N/C) * (0.09 m)^2 / (9 x 10^9 N m^2/C^2)

Simplifying the expression:

q = (825 N/C) * (0.0081 m^2) / (9 x 10^9 N m^2/C^2)

q = (0.0067125 C) / (9 x 10^9 N m^2/C^2)

q ≈ 7.46 x 10^-12 C

So, the magnitude of each point charge is approximately 7.46 x 10^-12 C.