Given below are two statements $:$ one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ Magnetic monopoles do not exist.
Reason $(R) :$ Magnetic field lines are continuous and form closed loops.
In the light of the above statements, choose the most appropriate answer from the options given below.

$(a)$ 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?

The unit of magnetic flux is

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)

Verify Gauss's law for the magnetic field of a point dipole of dipole moment $\vec{m}$ at the origin for a surface which is a sphere of radius $R$.

$A$ square of side $x \, m$ lies in the $x-y$ plane in a region where the magnetic field is given by $\vec B = B_0 (3\hat i + 4\hat j + 5\hat k ) \, T$,where $B_0$ is a constant. The magnitude of the magnetic flux passing through the square is: