Why does an infinite line of charge produce only a radial field?

[Seraph404]

"Stopping the Proton"

Homework Statement

An infinitely long line of charge has a linear charge density of 8.00×10−12 C/m. A proton is at distance 14.0 cm from the line and is moving directly toward the line with speed 1500 m/s.

I just want a better understanding of this statement:

"An infinite line of charge will generate a field with only a radial component."

Why, again? I can post more parts of the problem if that's too confusing.

 

[LowlyPion]

Because the line charge is infinite, the field lines will all be perpendicular to the wire - radially outward for plus charge - if for no other reason than that any calculation of the field will find as much charge to one side as to the other and any component of the field that might be calculated for charge on one side is canceled out by the field component from an equal charge an equal distance to the other. The equipotential surfaces will then be concentric cylinders.