Final answer:
The sideways deflection of a proton in a capacitor involves applying electromagnetism and kinematics principles. The electric field's strength determines the force on the proton, which, combined with the duration inside the field, would allow calculation of its deflection.
Step-by-step explanation:
The question is related to the deflection of a proton when it enters a region with an electric or magnetic field, such as the space between the plates of a parallel-plate capacitor. This is a clear case dealing with the principles of electromagnetism and kinematics. To calculate the sideways deflection of the proton at the far edge of the capacitor, one would need to use the force exerted by the electric field on the proton and determine the resulting acceleration and subsequent motion of the proton through the electric field.
For such a calculation, the electric field strength between the capacitor plates would be essential, which depends on the voltage across the capacitor and the separation of the plates. Given that this is a physics problem involving motion of charged particles and electric fields, principles such as Coulomb's Law, Newton's second law of motion, and the equations of motion would be relevant.
In the context of the problem provided, the actual numerical value of the deflection cannot be determined without additional specifics such as the magnitude of the electric field between the capacitor plates and the duration of the proton's exposure to this field.