How Do Forces Add in a Right Angled Triangle with Identical Charges?

[jevillan]

Homework Statement

Each corner of a right angled triangle is occupied by identical point charges "A", "B", and "C" repectively."A" exerts force F on "B". An equal force F is exerted by "C" on "B" (ÐABC=90°). Determine an expression for the net force on "B"?

Homework Equations

F = (kq1q2)/(d^2)

The Attempt at a Solution

Fa = (kQaQb)/d^2
Fc = (kQcQb)/d^2

Fnet = [(kQaQb)/d^2]-[(kQcQb)/d^2]
=(kQaQb) - (kQcQb)
= kQb(Qa-Qc)

I'm not sure if I did that right...I was trying to figure out what direction the net force would be in, but if the two forces are equal in magnitude, wouldn't the net force just be zero?

 

[Aimless]

Have you drawn a diagram of this problem?

What do the forces acting on B look like?

 

[jevillan]

Have you drawn a diagram of this problem?

What do the forces acting on B look like?

http://imageshack.us/photo/my-images/232/unledn.gif/
not quite sure if that's how I'm supposed to draw the forces ... :S

 

[Aimless]

Close enough.

Now, consider the point B, and diagram the forces acting upon it. Remember that forces are vectors. How do vectors add?

(When making a force diagram, we typically draw the forces as "arrows" originating from the object upon which they act, pointing in the direction in which the force acts, and with a length equal to the magnitude of the force. Think of it as if the arrows were "pulling" the object in the direction of the force. These arrows represent the force vectors acting upon the object in question. In this case, it would be two arrows originating from point B. Which way do they point? What are their lengths?)

 

[jevillan]

Close enough.

Now, consider the point B, and diagram the forces acting upon it. Remember that forces are vectors. How do vectors add?

(When making a force diagram, we typically draw the forces as "arrows" originating from the object upon which they act, pointing in the direction in which the force acts, and with a length equal to the magnitude of the force. Think of it as if the arrows were "pulling" the object in the direction of the force. These arrows represent the force vectors acting upon the object in question. In this case, it would be two arrows originating from point B. Which way do they point? What are their lengths?)

so that diagram would have two arrows coming from point B (one going down and one going to the right) and they would both be equal in length. Would the net force be the magnitude and direction of the displacement of those two vectors? (In this case, the magnitude would be 0 right?)

 

[Aimless]

so that diagram would have two arrows coming from point B (one going down and one going to the right) and they would both be equal in length.

Correct.

Would the net force be the magnitude and direction of the displacement of those two vectors? (In this case, the magnitude would be 0 right?)

The net force is the magnitude and direction of the sum of the force vectors acting on B.

How do vectors add? (Hint: How would you write each vector in terms of its components?)