Q. The charge per unit length of four quadrant of the ring of radius R is 2 lambda, -2 lambda, 1 lambda and -1 lambda respectively. The electric field at the centre is

(a) - (lambda/2pie epsilon R) i cap

(b) (lambda/2 pie epsilon R) j cap

(c) (square root (2)lambda/4 pie epsilon R) j cap

(d) None of the above

First draw the net force of electric field due to each segment of ring. Every sector of charge q(=lambda) will exert a net force F in the direction of 45 degrees with the x-axis.(The +ve x-axis is towards your right>>>)

The net force after each force cancels is 2Fcos45 along negative x-axis.

Therefore A) is the answer.