

This is with reference to Class 12 Physics Electric charges and fields video part 19. In this video discussion is about Electric field intensity due to infinite long conductor.
E = kλ/r (sin Ф1 + sin Ф2) is the final expression for electric field intensity due to infinite long conductor.
The vertical component cancels out only because of symmetry between the upper and the lower part. If lower part is not present, then the whole initial assumption is itself incorrect. In other words, the vertical component cancels out only because of the existence of both Ф1 and Ф2.

