Two concentric coplanar circular loops of radii $r_1$ and $r_2$ carry currents of respectively $i_1$ and $i_2$ in opposite directions (one clockwise and the other anticlockwise). The magnetic induction at the centre of the loops is half that due to $i_1$ alone at the centre. If $r_2 = 2r_1$,the value of $i_2/i_1$ is:

$A$ tightly wound $100$ turns coil of radius $10 \,cm$ carries a current of $7 \,A$. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4 \pi \times 10^{-7} \,SI$ units):

Two identical long parallel wires carry currents $I_1$ and $I_2$ such that $I_1 > I_2$. When the currents are in the same direction,the magnetic field at a point midway between the wires is $8 \times 10^{-6} \ T$. If the direction of $I_2$ is reversed,the field becomes $3.2 \times 10^{-5} \ T$. The ratio of $I_2$ to $I_1$ is

$A$ regular polygon of $6$ sides is formed by bending a wire of length $4 \pi \text{ m}$. If an electric current of $4 \pi \sqrt{3} \text{ A}$ is flowing through the sides of the polygon,the magnetic field at the centre of the polygon would be $x \times 10^{-7} \text{ T}$. The value of $x$ is . . . . . . .

Two parallel wires situated at a distance $2a$ are carrying equal currents $i$ in opposite directions as shown in the figure. The value of the magnetic field at a point $P$ situated at equal distances $r$ from both the wires will be:

As shown in the figure,two infinitely long straight parallel wires $P$ and $Q$ carrying equal currents in opposite directions are arranged parallel to the $Y$-axis. If the magnetic field due to wire $P$ at the origin '$O$' of the coordinate system is $B$,then match the resultant magnetic fields at various points given in Column $A$ with the points given in Column $B$.

Column $A$	Column $B$
$A) \frac{B}{4}$	$i) (0, 0)$
$B) \frac{B}{2}$	$ii) (a, 0)$
$C) \frac{2B}{3}$	$iii) (2a, 0)$
$D) 2B$	$iv) (3a, 0)$