Charge on a point in three different locations with a thin semicircular rod

[swagadoo]

Homework Statement

A thin semicircular rod is broken into two halves, the top half has a total charge +Q uniformly distributed along it, and the bottom half has a total charge -Q uniformly distributed along it.
http://imgur.com/tObt2V0

Homework Equations

Indicate the direction of the net electric force on a positive test charge placed in turn at points A, B, C.

The Attempt at a Solution

Had A's force vector pointing down and to the right, same with b and C pointing down and to the left but I am not sure about my answers.

 

[haruspex]

Think about the forces in the horizontal and vertical directions separately. E.g. for A, compare the horizontal forces (i.e. along the line AB) exerted by the two quadrants.

 

[swagadoo]

I can't really visualize it but my guess is that the horizontal component of +Q would be to the left and the -Q would have a horizontal component equal and opposite so to the right. The vertical component of +Q on the charges would be down, same with the -Q charge.

 

[haruspex]

Exactly so. So the resultant force is in which direction?

 

[swagadoo]

Down and to the right. Would it be the same for both A and B. And C would be down and to the right?

 

[swagadoo]

or is the resultant straight down?

 

[fgb]

If the horizontal components are opposite (and equal in magnitude, since all distances are the same for the + and for the - quadrant), don't they cancel each other?

 

[swagadoo]

If the horizontal components are opposite (and equal in magnitude, since all distances are the same for the + and for the - quadrant), don't they cancel each other?

yeah that's what I am thinking

 

[fgb]

Yeah, so the resultant is straight down, like you said :)

 

[swagadoo]

So all of the points; A,B, and C would have the same vector pointing down?

 

[fgb]

The magnitude of said vector would change according to distance from the point to the quadrants (i.e., the vector is smaller for point A than for point B), but it is indeed straight down for three points :)

 

[swagadoo]

Thank you very much.