$A$ metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at $t = 0$ and completely emerges out at $t = T \, \text{sec}$. The current in the ring varies as

$A$ copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring as shown in figure. The acceleration of the falling magnet is ($g=$ acceleration due to gravity)

Assertion : An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current.
Reason : The above statement is in accordance with the conservation of energy.

An insulated copper wire of $100$ turns is wrapped around a wooden cylindrical core of the cross-sectional area $24\,cm^2$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12\,\Omega$. If an externally applied uniform magnetic field in the core along its axis changes from $1.5\,T$ in one direction to $1.5\,T$ in the opposite direction,the charge flowing through a point in the circuit during the change of magnetic field will be $.........\,mC$.

$A$ uniform magnetic field $\vec{B}$ is perpendicular to the plane of a circular loop of diameter $10 \text{ cm}$ formed from a wire of diameter $2 \text{ mm}$ and resistivity $2 \times 10^{-8} \Omega \text{ m}$. If a current of $11 \text{ A}$ is to be induced in the loop, then the rate at which $\vec{B}$ is to be changed is: (in $\text{ T s}^{-1}$)

$A$ coil of $40 \ \Omega$ resistance has $100$ turns and a radius of $6 \ mm$. It is connected to an ammeter of resistance $160 \ \Omega$. The coil is placed perpendicular to a magnetic field. When the coil is taken out of the field,a charge of $32 \ \mu C$ flows through it. The intensity of the magnetic field is: (in $T$)