Q$3(20\%)$

A circular loop in the plane of the paper $(x-$y plane$)$ lies in a megnetic field of value vec$(B)=2$hat$(x)+2$hat$(z)$ Tesla. The loop's diameter changes from $100$ cm to $50$ cm in $2$ seconds while magnetic field changes to vec$(B)=4$hat$()$ Tesla.

a$)$ What is the initial flux passing through the loop? What is the final flux passing through the loop?

t$)$ What is the magnitude of the average induced emf$/$voltage$?($Hint the average induced EMF is given by $V=-\frac{}{t}$ where $\frac{O}{?}$ is the change in flux and $t$ the time it took the change to occur$)$

c$)$ If the coil resistance is $10,$ what is the average induced current?