Electric Fields Cancelling Out?

[Bashyboy]

Homework Statement

An example problem I am reading is about the electric field of a uniform ring of charge.

I attached the diagram provided in the problem.

What confuses me is that the electric field lines in the y-direction cancel out. Wouldn't the fields have to cross, if they were to cancel out? What does it even mean that they cancel out?

 

[rude man]

They do cross. It means for every +y force there is an equal and opposite -y force.

Pretend you have just a half ring. Then there will be a net y force at P. Then move the ring 180 degrees. Then the y force will be the same magnitude but in the opposite y direction. Hope that helps you see the situation.

 

[Bashyboy]

Yes, that is helpful, it just seems to contradict what I have been told, that electric fields lines aren't suppose to cross. What exactly is meant by that statement, that electric field lines can't cross?

 

[rude man]

Another example:

If I have one point charge I get a field. If I have 2 point charges the field is the (vector) sum due to the two charges. The fields exist independent of each other, and they add. If I put a unit charge inbetween the first two the force on the unit charge is the (vector) sum of the fields due to the first two charges. So the fields set up by the first two charges have to coexist at the point of the unit charge, right?

 

[haruspex]

What exactly is meant by that statement, that electric field lines can't cross?

You are considering a field as the sum of contributory fields. The lines from some contributions may well cross with others, but no lines will cross in the net field.