$3.$ Four long, parallel wires are located at the corners of a square of side $15$ cm and carry currents as shown in Fig. $3.$ Find: $(25$ points$)$

$($a$)$ the resultant magnetic field at the center of the square;

$($b$)$ the magnetic force on an electron moving at $\backslash (4\backslash$times $10^\{6\}\backslash$mathbf$\{$i ~$\}\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ as it passes the center.