Consider the following figure. $A$ uniform magnetic field of $0.2 \, T$ is directed along the positive $x-$axis. What is the magnetic flux through the top surface of the figure in $m-Wb$?

$(a)$ Magnetic field lines show the direction (at every point) along which a small magnetised needle aligns (at the point). Do the magnetic field lines also represent the lines of force on a moving charged particle at every point?
$(b)$ Magnetic field lines can be entirely confined within the core of a toroid,but not within a straight solenoid. Why?
$(c)$ If magnetic monopoles existed,how would the Gauss's law of magnetism be modified?
$(d)$ Does a bar magnet exert a torque on itself due to its own field? Does one element of a current-carrying wire exert a force on another element of the same wire?
$(e)$ Magnetic field arises due to charges in motion. Can a system have magnetic moments even though its net charge is zero?

Assertion $(A)$: Magnetic flux is a vector quantity.
Reason $(R)$: Value of magnetic flux can be positive, negative, or zero.

Explain Gauss's law for magnetism.

$A$ circular disc of radius $0.2 \; m$ is placed in a uniform magnetic field of induction $\frac{1}{\pi} \; Wb/m^2$ in such a way that its axis makes an angle of $60^{\circ}$ with $\vec{B}$. The magnetic flux linked with the disc is..... $Wb$.

Two circular loops of diameters $0.6 \,cm$ and $40 \,cm$ are kept coaxially with a separation of $15 \,cm$ between their centres. If a current $2 \,A$ flows through the smaller loop, then the flux linked with the bigger loop is (approximately)