$A$ circular loop of a wire and a long straight wire carry currents $I_c$ and $I_e$,respectively,as shown in the figure. Assuming that these are placed in the same plane,the magnetic field will be zero at the centre of the loop when the separation $H$ is:

Two infinitely long wires are placed at $(1 \text{ cm}, 1 \text{ cm})$ and $(1 \text{ cm}, -1 \text{ cm})$ with $1 \text{ A}$ current in each and in the same directions perpendicular to the $xy$-plane. Let the magnetic field due to these current-carrying wires at the origin be $B$. If $B_0$ is the magnitude of the field if only one of them was present,then $\frac{|B|}{B_0}$ is

$A$ conducting circular loop of copper is placed as shown in the figure. The cross-sectional area of part $abc$ is $A$ and that of part $adc$ is $A/3$. The magnetic field at point $O$ is:

$A$ current $I$ is flowing in a conductor $PQRST$ as shown in the figure. The radius of the curved path $QRS$ is $r$ and the length of the straight portions $PQ$ and $ST$ is very large. The magnetic field at the centre $O$ of the curved part is $(\mu_0 = \text{permeability of free space})$

$A$ thin charged rod is bent into the shape of a small circle of radius $R$, the charge per unit length of the rod being $\lambda$. The circle is rotated about its axis with a time period $T$, and it is found that the magnetic field at a distance $d$ away $(d >> R)$ from the center and on the axis varies as $\frac{R^{m}}{d^{n}}$. The values of $m$ and $n$ respectively are:

The magnetic field due to a current-carrying circular loop of radius $5 \ cm$ at a point on the axis at a distance of $12 \ cm$ from the centre is $250 \ \mu T$. The magnetic field at the centre of the loop is (in $\mu T$)