$2.$ A single current$-$carrying circular loop of radius $\backslash ($ R$=6\mathrm{.}4\backslash$mathrm$\{$~cm$\}\backslash )$ is placed next to a long straight wire as shown in Figure. A current $\backslash ($ i$\_\{1\}=-7\mathrm{.}6\backslash$mathrm$\{$~A$\}\backslash )$ is passing through the wire towards the right. At a certain moment, an electron is moving at a velocity $\backslash (\backslash$overrightarrow$\{$v$^\{\backslash$prime$\}\}=570\mathrm{.}0\backslash$mathrm$\{$j$\}\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash )$ toward the center of the circular wire. At the instant shown in figure $2,$ the electron's distance from the wire is $\backslash ($ d$=8\mathrm{.}5\backslash$mathrm$\{$~cm$\}\backslash ).$

Figure $2$

The $\backslash ($ z $\backslash )$ axis points out of the page in the coordinate system shown in the figure which is represented by the circle with a dot inside.

a$)$ Compute the magnitude of the magnetic field at the center $\backslash ($ c $\backslash )$ due to the current passing through the straight wire. $[1]$

b$)$ What is the magnitude of the magnetic field at the center $\backslash ($ c $\backslash )$ due to the motion of the electron? $[1]$

c$)$ In unit vector notation, find the magnetic force on the electron due to the current passing through the straight wire. $[2]$

d$)$ Calculate the magnitude and direction of the current to the circular wire to produce zero magnetic fields at its center c$.$ Consider counter$-$clockwise circulation of current as positive. $[1]$