Final answer:
The electric field at the midpoint between an electron and a proton will be the vector sum of the fields due to each. Given their opposite charges and equal magnitudes, the net electric field will point away from the electron towards the proton and have a magnitude that is twice that of the field due to a single charge.
Step-by-step explanation:
To find the magnitude and direction of the electric field at the midpoint between an electron and a proton, we first need to calculate the individual electric fields produced by each charge at that point. The electric field due to a point charge can be calculated using the formula:
E = k * Q / r^2
Where E is the electric field magnitude, k is the electrostatic constant (9.0 x 10^9 N m^2/C^2), Q is the charge, and r is the distance from the charge. In this case, both the electron and the proton have the same charge magnitude of 1.6 x 10^-19 C. The distance between them is 809 nm, which is equal to 809 x 10^-9 m.
Using this information, we calculate the electric field due to the electron and the proton at the midpoint. Since the charges have opposite signs, the electric fields will have opposite directions. The magnitude of the electric field at the midpoint is the sum of the magnitudes of the electric fields produced by the electron and the proton.
The direction of the electric field at the midpoint is determined by the direction of the net force experienced by a positive test charge placed at that point.