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 $, A$)?

$A$ 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:

Figure shows a uniform magnetic field $B$ confined to a cylindrical volume and increasing at a constant rate. The instantaneous acceleration experienced by an electron placed at $P$ is

In the diagram shown,a time-varying non-uniform magnetic field passes through a circular region of radius $R$. The magnetic field is directed outwards and it is a function of radial distance $r$ and time $t$ according to the relation $B = B_0rt$. What is the induced electric field strength at a radial distance $R/2$ from the center?

$A$ line charge $\lambda$ per unit length is lodged uniformly onto the rim of a wheel of mass $M$ and radius $R$. The wheel has light non-conducting spokes and is free to rotate without friction about its axis. $A$ uniform magnetic field extends over a circular region within the rim. It is given by,
$B = -B_{0} \hat{k}$ for $r \leq a$ (where $a < R$)
$B = 0$ otherwise.
What is the angular velocity of the wheel after the field is suddenly switched off?

$A$ 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.