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

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.

The Attempt at a Solution

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haruspex
Homework Helper
Gold Member
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.

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
Homework Helper
Gold Member
Exactly so. So the resultant force is in which direction?

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

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?

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 thats what im thinking

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

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 :)

Thank you very much.