$A$ long wire lies along the $X$-axis and carries a current of $40 \, A$ in the positive $x$-direction. $A$ second long wire is perpendicular to the $xy$-plane, passes through the point $(3.0 \, m) \hat{j}$, and carries a current along the positive $z$-direction. If the magnitude of the resultant magnetic field at the point $(2.0 \, m) \hat{j}$ is $R=5 \times 10^{-6} \, T$, then the current in the second wire is (Permeability of free space, $\mu_0=4 \pi \times 10^{-7} \, T \cdot m/A$) (in $A$)

$A$ steady current $I$ flows through a wire loop $PQR$ having the shape of a right-angled triangle with $PQ = 3x$, $PR = 4x$, and $QR = 5x$. If the magnitude of the magnetic field at $P$ due to this loop is $k \left( \frac{\mu_0 I}{48 \pi x} \right)$, find the value of $k$.

Given below are two statements:
Statement $I:$ Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element $(Id\vec{l})$ of a current-carrying conductor only.
Statement $II:$ Biot-Savart's law is analogous to Coulomb's inverse square law of charge $q$,with the former being related to the field produced by a vector source,$Id\vec{l}$,while the latter is produced by a scalar source,$q$. In light of the above statements,choose the most appropriate answer from the options given below:

An infinitely long straight conductor is bent into the shape as shown below. It carries a current of $I$ ampere and the radius of the circular loop is $R$ metre. Then,the magnitude of magnetic induction at the centre of the circular loop is

Consider a tightly wound $100$ turn coil of radius $10 \,cm$ carrying a current of $2 \,A$. The magnitude of the magnetic field at the centre of the coil is

$A$ battery is connected between two points $A$ and $B$ on the circumference of a uniform conducting ring of radius $r$ and resistance $R$. One of the arcs $AB$ of the ring subtends an angle $\theta$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is