Flux $\phi$ (in weber) in a closed circuit of resistance $10 \, \Omega$ varies with time $t$ (in $s$) according to the equation $\phi = 6t^2 - 5t + 1$. What is the magnitude of the induced current at $t = 0.25 \, s$ (in $, A$)?

$A$ solenoid of radius $R$ and length $L$ has a current $I = I_0 \sin \omega t$. The value of the induced electric field at a distance $r$ inside the solenoid is:

$A$ uniform magnetic field $B$ exists in a cylindrical region of radius $10\,cm$ as shown in the figure. $A$ uniform wire of length $80\,cm$ and resistance $4.0\,\Omega$ is bent into a square frame and is placed with one side along a diameter of the cylindrical region. If the magnetic field increases at a constant rate of $0.010\,T/s$,find the current induced in the frame.

$A$ uniform but time-varying magnetic field $B(t)$ exists in a circular region of radius $a$ and is directed into the plane of the paper,as shown. The magnitude of the induced electric field at point $P$ at a distance $r$ $(r > a)$ from the centre of the circular region is:

$A$ metallic ring of radius $a$ and resistance $R$ is held fixed with its axis along a spatially uniform magnetic field whose magnitude is $B = B_0 \sin \omega t$. Gravity is neglected. Then,

$A$ long circular tube of length $10 \ m$ and radius $0.3 \ m$ carries a current $I$ along its curved surface as shown. $A$ wire-loop of resistance $0.005 \ \Omega$ and of radius $0.1 \ m$ is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as $I = I_0 \cos(300t)$ where $I_0$ is constant. If the magnetic moment of the loop is $N \mu_0 I_0 \sin(300t)$,then $N$ is: