The figure shows a metallic square frame of edge in a vertical plane. A uniform magnetic field $B$ exists int he space in a direction perpendicular to the plane of the figure. Two boys pull the opposite corners of the square to deform it into a rhombus. They start pulling the corners at $t=0$, and displace the corners at a uniform speed $u$.

$\left(a\right)$ Find the induced emf in the frame at the instant, when the angles at these corners reduce to $60°$. 

$\left(b\right)$ Find the induced current in the frame at the instant if the total resistance of the frame is $R$.

$\left(c\right)$ Find the total charge which flows through a side of the frame by the time the square is deformed into a straight line.

The magnetic field in the cylindrical region shown in figure increases at a constant rate of $20.0 \mathrm{mT} {\mathrm{s}}^{-1}$. Each side of the square loop $abcd$, and $defa$ has a length of $1.00 \mathrm{cm}$ and a resistance of $4.00 \mathrm{\Omega }$. Find the current (magnitude and sense) in the wire if $\left(a\right)$ the switch $S_1$ is closed but $S_2$ is open $\left(b\right)$ $S_1$, $S_2$ is closed, $\left(c\right)$ both $S_1$ and $S_2$ are open and $\left(d\right)$ both $S_1$ and $S_2$ are closed.

For the wire arrangement in the figure, $a=12.0 \mathrm{cm}$ and $b=16.0 \mathrm{cm}$.
The current in the long straight wire is $i=6.50t^2-10.0t$, where $i$ is in amperes and $t$ is in seconds. (a) Find the emf in the square loop at $t=3.00 \mathrm{s}$.
(b) What is the direction of the induced current in the loop?

In given figure, two straight conducting rails form a right angle. A conducting bar in contact with the rails starts at the vertex at time $t=0$ and moves with a constant velocity of $8.90 \mathrm{m} {\mathrm{s}}^{-1}$ along them. A magnetic field with $B=0.350 \mathrm{T}$ is directed out of the page. Calculate $\left(\mathrm{a}\right)$ the flux through the triangle formed by the rails and bar at $t=3.00 \mathrm{s}$and $\left(\mathrm{b}\right)$ the emf around the triangle at that time.$\left(c\right)$ If the emf is $\epsilon =a{t}^n,$ where $a$ and $n$ are constants, what is the value of $n ?$ 

Figure shows a closed surface. Along the flat top face, which has a radius of $2.0 \mathrm{cm}$. A perpendicular magnetic field $\overrightarrow{B}$ of magnitude $0.50 \mathrm{T}$ is directed outward. Along the flat bottom face, a magnetic flux of $0.70 \mathrm{mWb}$ is directed outward. What are the $\left(a\right)$ magnitude and $\left(b\right)$ direction (inward or outward) of the magnetic flux through the curved part of the surface?