A loop, made of straight edges has six corners at $A(0,0,0), B(L, 0,0)$, $C(L, L, 0), D(0, L, 0), E(0, L, L)$ and $F(0,0, L)$. A magnetic field $\mathbf{B}=B_0(\hat{\mathbf{i}}+\hat{\mathbf{k}}) \mathrm{T}$ is present in the region. The flux passing through the loop $A B C D E F A$ (in that order) is

A cylindrical bar magnet is rotated about its axis. A wire is connected from the axis and is made to touch the cylindrical surface through a contact. Then,

There are two coils $A$ and $B$ as shown in figure. $A$ current starts flowing in $B$ as shown, when $A$ is moved towards $B$ and stops when $A$ stops moving. The current in $A$ is counter clockwise. $B$ is kept stationary when $A$ moves. We can infer that

Same as problem 4 except the coil $A$ is made to rotate about a vertical axis (figure). No current flows in $B$ if $A$ is at rest. The current in coil $A$, when the current in $B($ at $t=0)$ is counter-clockwise and the coil $A$ is as shown at this instant, $t=0$, is

The self inductance $L$ of a solenoid of length $l$ and area of cross-section $A$, with a fixed number of turns $N$ increases as