$A$ square loop of side $2 \ m$ lies in the $Y-Z$ plane in a region having a magnetic field $\vec{B}=(5 \hat{i}+3 \hat{j}-4 \hat{k}) \ T$. The magnitude of magnetic flux through the square loop is (in $Wb$)

$A$ 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.

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.

Which of the following do not exist?

$A$ circular loop of radius $R$ carrying current $I$ lies in the $x-y$ plane with its centre at the origin. The total magnetic flux through the $x-y$ plane is:

An infinitely long wire lying along the $Y$-axis carries a current $I$ as shown in the figure. What is the magnetic flux through a circular loop of radius $R$ in the $xy$-plane? [Assume $\mu_0$ is the magnetic permeability of free space.]