Answer: c) -i
Explanation:
Since the particles carry the same charges they will all repel each other,
Since the particles are at equal distance from each other, the magnitude of their repelling forces on each other will be equal assuming they are all of equal mass.
Each perticle will move away at a 90° direction from the center and this puts the electric field at the center to sum up to zero.
All field will point towards the point of least potential hence the electric field at point (1, - 1) will point towards -I direction which is along the x-axis towards the zero point.
Mathematically, force on each particle Fp = -Qq/r^2 (coulumb's law)
Assuming each has a charge of 1C
The force field between point (1, 0) and point (-1, 1) or (-1, - 1) will vary as inverse square of their distance,
Since they are 5 units apart (length of their diagonal), they experience a repulsion of the magnitude 0.04 (1/25)
For points (1, 0) and (1, 1) or (1, - 1) the magnitude is 1 since they are 1 unit apart. This is 25 times stronger than for the above.
This means the field will move towards the lesser field which is toward -i
See image below