Answer
We can rank the four situations according to the magnitude of the net force on the central proton:
$1 = 2 \gt 3 = 4$
Work Step by Step
We can write an expression for the force between two charged particles:
$F = \frac{q_1~q_2}{4\pi~\epsilon_0~r^2}$
Note that the charge of a proton and a charge of an electron have the same magnitude.
In situation (1), the vertical components of the forces on the central proton due to the other particles cancel out. The horizontal components of the forces on the central proton are all directed in the positive x direction. Therefore, the net force is in the positive x direction and the net force is a maximum since all the horizontal components of the forces are in the same direction.
In situation (2), the vertical components of the forces on the central proton due to the other particles cancel out. The horizontal components of the forces on the central proton are all directed in the positive x direction. Therefore, the net force is in the positive x direction and the net force is a maximum since all the horizontal components of the forces are in the same direction.
In situation (3), the vertical components of the forces on the central proton due to the other particles cancel out. The horizontal components of the forces on the central proton due to the protons are directed in the positive x direction. The horizontal components of the forces on the central proton due to the electrons are directed in the negative x direction. Since the magnitude of the horizontal components of the forces due to the protons is greater than the magnitude of the horizontal components of the forces due to the electrons, the net force is in the positive x direction, but the net force is not a maximum since not all the horizontal components of the forces are in the same direction.
In situation (4), the vertical components of the forces on the central proton due to the other particles cancel out. The horizontal components of the forces on the central proton due to the protons are directed in the positive x direction. The horizontal components of the forces on the central proton due to the electrons are directed in the negative x direction. Since the magnitude of the horizontal components of the forces due to the electrons is greater than the magnitude of the horizontal components of the forces due to the protons, the net force is in the negative x direction, but the net force is not a maximum since not all the horizontal components of the forces are in the same direction.
We can rank the four situations according to the magnitude of the net force on the central proton:
$1 = 2 \gt 3 = 4$
