$A$ coil of $100$ turns and area $5 \text{ cm}^2$ is placed in a magnetic field $B = 0.2 \text{ T}$. The normal to the plane of the coil makes an angle of $60^o$ with the direction of the magnetic field. The magnetic flux linked with the coil is:

$A$ uniform magnetic field of strength $B=2 \text{ mT}$ exists vertically downwards. These magnetic field lines pass through a closed surface as shown in the figure. The closed surface consists of a hemisphere $S_1$,a right circular cone $S_2$,and a circular surface $S_3$. The magnetic flux through $S_1$ and $S_2$ are respectively:

Consider a closed loop $C$ in a magnetic field as shown in the figure. The flux passing through the loop is defined by choosing a surface whose edge coincides with the loop and using the formula $\phi = \sum \vec{B}_i \cdot d\vec{A}_i$. Now,if we choose two different surfaces $S_1$ and $S_2$ having $C$ as their edge,would we get the same answer for the magnetic flux? Justify your answer.

Imagine rolling a sheet of paper into a cylinder and placing a bar magnet near its end as shown in the figure. What can you say about the sign of $\vec B \cdot d\vec A$ for every area element $d\vec A$ on the surface of the cylinder?

$(a)$ 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?

In which of the following systems of units is $Weber$ the unit of magnetic flux?