Answer
$E_{A}=6.74\times10^6\frac{N}{C}$ up
$E_{B}=1.01\times10^6\frac{N}{C}$, $65.8^o$
$\theta_B=\arctan\big(\frac{6.78}{7.40}\big)=65.8^o$
Work Step by Step
$r_{A1,2}=\sqrt{(0.1m)^2+(0.05m)^2}=0.112m$
$r_{B1}=\sqrt{(0.05m)^2+(0.05m)^2}=0.071m$
$r_{B2}=\sqrt{(0.15m)^2+(0.05m)^2}=0.158m$
$E_{A}=2(9.0\times10^9\frac{Nm^2}{C^2})\frac{4.7\mu C}{(0.112m)^2}=6.74\times10^6\frac{N}{C}$ up
$E_{B}=(9.0\times10^9\frac{Nm^2}{C^2})\bigg(\frac{4.7\mu C}{(0.071m)^2}+\frac{4.7\mu C}{(0.158m)^2}\bigg)$
$=1.01\times10^7\frac{N}{C}$
$E_{Bx}=k\bigg(\frac{4.7\mu C}{(0.071m)^2}\cos(45^o)+\frac{4.7\mu C}{(0.158m)^2}\cos(30^o)\bigg)$
$=7.40\times10^6\frac{N}{C}$
$E_{By}=k\bigg(\frac{4.7\mu C}{(0.071m)^2}\sin(45^o)+\frac{4.7\mu C}{(0.158m)^2}\sin(30^o)\bigg)$
$=6.78\times10^6\frac{N}{C}$
$\theta_B=\arctan\big(\frac{6.78}{7.40}\big)=65.8^o$
