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Physics: Post your doubts here!

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When there is no air resistance, horizontal component always remains the same.
Where there is air resistance, horizontal component decreases.
But then the question said that air resistance is ignored... so then shouldn't horizontal component always remains the same :p
Or do you mean the other way round?
 
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Because these two points are exactly the same distance away from the point charge. Thus, the force pulling them is the same in both the positions. No work is done when moving it from P to Q along a path where the distance from the pulling force remains the same. This is because the electric potential energy in both positions is exactly the same.

For example, the moon does no work when it orbits the earth.
The earth does no work when it orbits the sun. This is because no change in gravitational potential energy occurs.
 
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