An equilateral triangle has a point charge +q at each of the three vertices (A, B, C). Another point charge Q is placed at D, the midpoint of the side BC. What is the charge Q if the total electric force on the charge at A due to the charges at B, C, and D is zero? (Use any variable or symbol stated above as necessary.)
The Attempt at a Solution
The total net force on A is zero.
Let's say the length of AB and AC are d so that the distance of B and C to A are d. Now, we have to find the distance between Q and A. Well, Q is placed in the midpoint of BC, so that we can bisect the triangle by drawing a line through A and Q. That makes a 30-60-90 triangle in which the hypotenuse is d. Using trigonometry, we know that QB and QC are d/2, making QA (d*sqrt(3))/2.
[ k(+q)(+q)/d² ] + [ k(+q)(+q)/d² ] + [ k(Q)(+q)/((d*sqrt(3))/2)² ]
To make the math easier, take out the common factor k(+q) and solve ((d*sqrt(3))/2)
k(+q) [ (+q)/d² + (+q)/d² +(Q)/(3d²/4) ]
So, +2q/d² + (Q)/(3d²/4) = 0
+2q/d² = -(Q)/(3d²/4)
Multiply 3d² and divide 4 to the other side
+2q(3d²)/4d² = -Q
d² cancels out, multiply both sides by -1
Q = -(3/2)q
Webassign says it's wrong. Can you think of any way I can rearrange it? Or is it done entirely wrong?