$A$ square loop of side $1\,m$ and resistance $1\,\Omega$ is placed in a magnetic field of $0.5\,T$. If the plane of the loop is perpendicular to the direction of the magnetic field,the magnetic flux through the loop is $\dots\dots$ weber.

$A$ long straight wire carrying a constant current $i$ is placed in the same plane as a rectangular loop of length $l$. The distance of the sides of the loop from the wire are $r_1$ and $r_2$. If the area under the curve of the magnetic field $B$ versus distance $r$ graph between $r_1$ and $r_2$ is $A$,find the magnetic flux through the loop.

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 $R$.

$A$ 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:

The magnetic flux linked with a closed coil is increased to a maximum value in $2 \,s$ and its relation with time is $\phi = at^2 + bt + c$. Then the relation between $a, b$ and $c$ is:

$A$ square of side $L$ meter lies in the $x-y$ plane in a region where the magnetic field is given by $\overrightarrow{B} = B_0(2 \hat{i} + 4 \hat{j} + 3 \hat{k}) \text{ T}$,where $B_0$ is a constant. The magnitude of the magnetic flux passing through the square is . . . . . . .