The negative sign in Faraday's law represents which fact?

$A$ coil of resistance $400 \Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (Wb) linked with the coil varies with time $t$ $(s)$ as $\phi = 50t^2 + 4$,the current in the coil at $t = 2 \ s$ will be: (in $A$)

$A$ long solenoid has $20$ turns per cm. $A$ small loop of area $\frac{4}{\pi} \text{ cm}^2$ is placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $1.0 \text{ A}$ to $3.0 \text{ A}$ in $0.2 \text{ s}$,what is the magnitude of the induced emf in the loop while the current is changing (in $\mu \text{V}$)?

It is desired to measure the magnitude of the magnetic field between the poles of a powerful loudspeaker magnet. $A$ small flat search coil of area $2 \; cm^{2}$ with $25$ closely wound turns is positioned normal to the field direction and then quickly snatched out of the field region. (Equivalently,one can give it a quick $90^{\circ}$ turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to the coil) is $7.5 \; mC$. The combined resistance of the coil and the galvanometer is $0.50 \; \Omega$. Estimate the field strength of the magnet.

Two identical circular coils $A$ and $B$ are kept on a horizontal tube side by side without touching each other. If the current in the coil $A$ increases with time,in response,the coil $B$

The magnitude of flux linked with a coil varies with time as $\phi = 3t^2 + 4t + 7$. The magnitude of the induced e.m.f. at $t = 2 \ s$ is: (in $V$)