The magnetic flux linked to a circular coil of radius \(R\) is given by:
\(\phi=2t^3+4t^2+2t+5\) Wb.
What is the magnitude of the induced EMF in the coil at \(t=5\) s?

A \(800\) turn coil of effective area \(0.05~\text{m}^2\) is kept perpendicular to a magnetic field \(5\times 10^{-5}~\text{T}\). When the plane of the coil is rotated by \(90^{\circ}\)$$around any of its coplanar axis in \(0.1~\text{s}\), the emf induced in the coil will be:

A long solenoid of diameter \(0.1\) m has \(2 \times 10^4\) turns per meter. At the center of the solenoid, a coil of \(100\) turns and radius \(0.01\) m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to \(0\) A from \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\), then the total charge flowing through the coil during this time is:
1. \(16~\mu \text{C}\)
2. \(32~\mu \text{C}\)
3. \(16\pi~\mu \text{C}\)
4. \(32\pi~\mu \text{C}\)

A uniform magnetic field is restricted within a region of radius \(r\). The magnetic field changes with time at a  rate \(\frac{dB}{dt}\). Loop \(1\) of radius \(R>r\) is enclosed within the region \(r\) and loop \(2\) of radius \(R\) is outside the region of the magnetic field as shown in the figure. Then, the emf generated is:
           

An electron moves on a straight-line path \(XY\) as shown. The \({abcd}\) is a coil adjacent to the path of electrons. What will be the direction of current if any, induced in the coil?