Find the magnetic field at point $P$ due to a straight line segment $AB$ of length $6\, cm$ carrying a current of $5\, A$. (See figure) $(\mu_0 = 4\pi \times 10^{-7}\, T\cdot m/A)$

$A$ long straight wire of circular cross-section is made of a non-magnetic material. The wire is of radius $a$. The wire carries a current $I$ which is uniformly distributed over its cross-section. The energy stored per unit length in the magnetic field contained within the wire is

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:

Two infinitely long parallel wires carry currents of magnitude $I_1$ and $I_2$ and are at a distance $4 \, cm$ apart. The magnitude of the net magnetic field is found to reach a non-zero minimum value between the two wires at a distance of $1 \, cm$ from the first wire. The ratio of the two currents and their mutual direction is

Two identical coils of radius $R$ and number of turns $N$ are placed perpendicular to each other such that they have a common center. The currents through them are $I$ and $I\sqrt{3}$. The resultant intensity of the magnetic field at the center of the coils will be:

$A$ current carrying circular coil of radius $R$ has a point $P$ situated on its axis at a distance $x$ from its centre $O$ of the coil. The magnetic induction at point $P$ is $\left(\frac{1}{8}\right)^{\text{th}}$ of the magnetic field at its centre $O$. The value of $x$ is