$A$ long straight rod of diameter $4 \text{ mm}$ carries a steady current '$i$'. The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances $1 \text{ mm}$ and $4 \text{ mm}$ from the axis of the rod is

$A$ long straight wire along the $z$-axis carries a current $I$ in the negative $z$-direction. The magnetic vector field $\vec{B}$ at a point having coordinates $(x, y)$ in the $z = 0$ plane is

If the strength of the magnetic field produced $10\,cm$ away from an infinitely long straight conductor is ${10^{ - 5}}\,Wb/m^2$,the value of the current flowing in the conductor will be........$A$.

$A$ long conducting wire carrying a current $I$ is bent at $120^{\circ}$ (see figure). The magnetic field $B$ at a point $P$ on the angle bisector of the bend at a distance $d$ from the bend is ($\mu_{0}$ is the permeability of free space):

$A$ long straight wire carrying current $16 \,A$ is bent at $90^{\circ}$ such that one segment lies along the positive $x$-axis and the other segment lies along the positive $y$-axis. What is the magnitude of the magnetic field at the point $P(-2 \,mm, 0)$ (in $\,mT$)? (Assume $\frac{\mu_0}{4 \pi} = 10^{-7} \,T \cdot m/A$)

The magnetic field at the centre of a circular coil of radius $r$ carrying current $I$ is $B_1$. The field at the centre of another coil of radius $2r$ carrying the same current $I$ is $B_2$. The ratio $\frac{B_1}{B_2}$ is