$12)$ The figure below shows two circular regions $R_1$ and $R_2$ with radii $r_1=23\mathrm{.}4cm$ and $r_2=31\mathrm{.}7cm.$ In $R_1$ there is a uniform magnetic field of magnitude $B_1=51\mathrm{.}4mT$ directed into the page, and in $R_2$ there is a uniform magnetic field of magnitude $B_2=75\mathrm{.}1mT$ directed out of the page $($ignore fringing$).$ Both fields are decreasing at the rate of $8\mathrm{.}60m\frac{T}{s}.$ Calculate $o{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$vec$(E)*dvec(s)$ for $($a$)$ path $1,($b$)$ path $2,$ and $($c$)$ path $3.$

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