Two parallel wires carry currents $i_1$ and $i_2$ $(i_1 > i_2)$. When the currents are in the same direction,the magnetic field at a point midway between the wires is $10 \, \mu T$. When the direction of $i_2$ is reversed,the magnetic field at that point becomes $30 \, \mu T$. What is the ratio $\frac{i_1}{i_2}$?

$A$ loop $ABCDA$,carrying current $I=12 \ A$,is placed in a plane,consists of two semi-circular segments of radius $R_1=6 \pi \ m$ and $R_2=4 \pi \ m$. The magnitude of the resultant magnetic field at center $O$ is $k \times 10^{-7} \ T$. The value of $k$ is . . . . . . . (Given $\mu_0=4 \pi \times 10^{-7} \ Tm \ A^{-1}$)

$A$ long straight wire of radius $a$ carries a steady current $I$. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ from the axis of the wire is:

Two infinitely long wires, each carrying a current $I = 10 \ A$, are bent to form a right angle as shown in the figure. Find the magnetic induction at point $O$. $\left[\mu_0 = 4\pi \times 10^{-7} \ H \ m^{-1}\right]$

$A$ long straight wire carrying a current of $30 \ A$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} \ T$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 \ cm$ away from the wire is $(\mu_0 = 4 \pi \times 10^{-7} \ H/m)$.

Two infinite wires bent in the form of an $L$ shape carry current $I$ as shown. What is the magnetic field at $O$?