A wire of infinite length carrying current $I$ lies along the z-axis. A square loop of side $\ell$ is placed such that the plane of the loop makes an angle $74°$ with the positive $x-$axis at $\left(\ell ,0,0\right)$ and side $AB$ touches the $x-$axis and parallel to $z-$axis as shown in the figure. The magnetic flux passing through the loop is $\frac{k{\mu }_0\ell }{\pi }$. Find the value of $k$. [take $I=10 \mathrm{A}, \ln \left(1.6\right)=0.47$ and $\tan 37°=\frac{3}{4}$]

In a coil of resistance $100 \mathrm{\Omega }$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:

A square-shaped conducting wire loop of dimension a moving parallel to the $x$-axis approaches a square region of size $b(a<b)$ where a uniform magnetic field $B$ exists pointing into the plane of the paper (see figure). As the loop passes through this region, the plot correctly depicting its speed $\left(v\right)$ as a function of $x$ is.