While demonstrating Faraday$$s law to her class, a physics professor inadvertently moves the gold ring on her finger from a location where a $0\mathrm{.}60-$T magnetic field points along her finger to a zero$-$field location in $45$ ms$.$ The $1\mathrm{.}5-$cm$-$diameter ring has a resistance and mass of $55$ m$$ and $15$ g$,$ respectively. $($a$)$ Estimate the thermal energy produced in the ring due to the flow of induced current. $($b$)$ Find the temperature rise of the ring, assuming all of the thermal energy produced goes into increasing the ring$$s temperature. The specific heat of gold is $129$ J$>$kg $$ C$.$