Let's name the variables we know and those we need:
q1: first charge; q1 = 9.12*10^-9 C
q2: second charge; q2 = -2.78*10^-9 C
r: distance between midpoint and the charges; r = 0.0499/2 = 0.02495 m
k: Coulomb's constant; k = 8.99*10^9
B1: field strength caused by first charge
B2: field strength caused by second
B1 = k|q1|/r^2 = 8.99*10^9*9.12*10^-9/0.02495^2
B1 = 131708.387 N/C
B2 = k|q2|/r^2 = 8.99*10^9*2.78*10^-9/0.02495^2
B2 = 40147.951 N/C
B = B1+B2 = 131708.387+40147.951 = 171856.338 N/C = 1.71856*10^5 N/C