A 12.4 nC charge is located at position (x,y)= 1.0cm, 2.0cm
A) At what (x,y) position is the electric field 225,000i N/C?
B) At what (x,y) position is the electric field (161,000i + 80,500j) N/C?
C) At what (x,y) position is the electric field (21,600i – 28,800j) N/C?
1 Answer

The general formula is E = kq/r^2 ==> r = sqrt(kq/E)
To keep the formulas uncluttered, I’m going to drop the i+j notation, so, e.g., the charge location = (1,2) cm.
Since q is positive, the signs of the components of r = those of E.
For each of the three cases:
Define a and b as the x and y components respectively of vector E (e.g., for case A, a = 225000, b = 0)
E = sqrt(a^2+b^2) N/C
Solve for r using formula above
deltar (x,y) = r*(a, b)/E cm
position (x,y) = deltar+(1, 2) cm
Be careful with signs.