A wire on a circuit board has a length L$=4\mathrm{.}9$mmL$=4\mathrm{.}9$mm and carries a current I$=2\mathrm{.}33$AI$=2\mathrm{.}33$A in the positive yy direction. A nearby circuit element generates a magnetic field in the vicinity of the wire given by

B$==$Bxi$^+$Byj$^+$Bzk$^(1\mathrm{.}1$G$)$i$^+(6\mathrm{.}4$G$)$j$^+(6\mathrm{.}3$G$)$k$^$B$=$Bxi$^+$Byj$^+$Bzk$^=(1\mathrm{.}1$G$)$i$^+(6\mathrm{.}4$G$)$j$^+(6\mathrm{.}3$G$)$k$^$

$$ Part $($a$)$

Calculate the magnitude of the magnetic field, in gauss, in the vicinity of the wire due to the circuit element.