$4.(30$ points$)$ CH$.29.$ See sections $29\mathrm{.}2,29\mathrm{.}3.$ and $29\mathrm{.}5.$ A mathematical, circular loop of diameter $\backslash (\backslash$mathrm$\{$d$\}=1\mathrm{.}0\backslash$mathrm$\{$~m$\}\backslash )$ exists in a region of space of a spatially uniform magnetic field where a uniform magnetic field everywhere is perpendicular to the plane of the loop. The magnetic field vector points into the page everywhere. The magnetic field magnitude is increasing at a rate of $\backslash (0\mathrm{.}698\backslash$mathrm$\{$~T$\}/\backslash$mathrm$\{$s$\}\backslash ).$

$($a$)(15$ points$)$ What is the direction of the induced electric field at the point $\backslash ($ P $\backslash )$ shown on the loop, left or right? Please indicate this direction by drawing an arrow at that point.

$($b$)(15$ points$)$ What is the magnitude of the induced electric field at the point $\backslash ($ P $\backslash )$ shown?