A rectangular loop with sides of length a$=1\mathrm{.}60$ cm and b$=2\mathrm{.}50$ cm is placed near a wire that carries a current that varies as a function of time: it$=2\mathrm{.}38+1\mathrm{.}05$t$2$ where the current is in Amperes and the time is in seconds. The distance from the straight wire to the closest side of the loop is d$=0\mathrm{.}560$ cm$.$

What is the magnetic flux through the loop at time t$=1\mathrm{.}90$ seconds? $($Define positive flux into the page.$)$

The magnetic flux is the surface $($area$)$ integral of magnetic field over the loop.

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What is the induced e$.$m$.$f$.$ in the loop at time t$=1\mathrm{.}90$ seconds? $($Note that positive emf is clockwise.$)$

Compute the rate of change of magnetic flux through the loop to get the e$.$m$.$f$..$