An infinite number of straight wires,each carrying current $I$,are equally placed as shown in the figure. Adjacent wires have current in opposite directions. The net magnetic field at point $P$ is:

The electric current in a circular coil of $2$ turns produces a magnetic induction $B_{1}$ at its centre. The coil is unwound and is rewound into a circular coil of $5$ turns and the same current produces a magnetic induction $B_{2}$ at its centre. The ratio of $\frac{B_{2}}{B_{1}}$ is:

$A$ and $B$ are two concentric circular loops carrying currents $i_1$ and $i_2$ as shown in the figure. If the ratio of their radii is $1:2$ and the ratio of the magnetic flux densities at the centre $O$ due to $A$ and $B$ is $1:3$,then the value of $\frac{i_1}{i_2}$ will be

$A$ current loop, having two circular arcs joined by two radial lines, is shown in the figure. It carries a current of $10 \, A$. The magnetic field at point $O$ will be close to:

Two long straight conductors with currents $I_1$ and $I_2$ are placed along $X$ and $Y$-axes respectively. The equation of the locus of points of zero magnetic induction is:

Two infinitely long straight wires lie in the $xy$-plane along the lines $x=+R$ and $x=-R$. The wire located at $x=+R$ carries a constant current $I_1$ and the wire located at $x=-R$ carries a constant current $I_2$. A circular loop of radius $R$ is suspended with its centre at $(0,0, \sqrt{3} R)$ and in a plane parallel to the $xy$-plane. This loop carries a constant current $I$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $+\hat{j}$ direction. Which of the following statements regarding the magnetic field $\vec{B}$ is (are) true?
$(A)$ If $I_1=I_2$, then $\vec{B}$ cannot be equal to zero at the origin $(0,0,0)$.
$(B)$ If $I_1 > 0$ and $I_2 < 0$, then $\vec{B}$ can be equal to zero at the origin $(0,0,0)$.
$(C)$ If $I_1 < 0$ and $I_2 > 0$, then $\vec{B}$ can be equal to zero at the origin $(0,0,0)$.
$(D)$ If $I_1=I_2$, then the $z$-component of the magnetic field at the centre of the loop is $\left(-\frac{\mu_0 I}{2 R}\right)$.