The correct option is
D x<−aWe know that, electric field due to a point charge is given by,
E=kQr2 [E∝Q and E∝1r2]
For point
O(−a<x<a), direction of electric field due to both charges will be same, so net electric field cannot be zero for
−a<x<a.
At point
A(x>a), direction of electric field due to both charges are in opposite directions.
But, magnitude of electric field due to
+2q charge will be greater as magnitude of charge is greater than
−q and also distance is less than that of
−q.
Therefore, net electric field cannot be zero for
x>a as well.
At point
B(x<−a), direction of electric field due to both charges are in opposite directions and also magnitude of electric field may become equal as distance is less for charge
−q, so it may compensate for the effect of smaller value of charge.
Hence, for some point
B(x<−a), the net electric field will be zero.