The magnitude of magnetic induction at the midpoint '$O$' due to the current arrangement shown in the figure is ($\mu_0$ = permeability of free space).

$A$ long curved conductor carries a current $I$. $A$ small current element of length $dl$ on the wire induces a magnetic field at a point away from the current element. If the position vector between the current element and the point is $\vec{r}$, making an angle $\theta$ with the current element, then the induced magnetic field density $d\vec{B}$ at the point is $(\mu_0 = \text{permeability of free space})$:

$A$ current carrying circular coil of radius $R$ produces magnetic field $B_1$ at an axial point $P$ at a distance $x$ from its centre and $B_2$ at point $Q$ placed at its centre respectively. If $B_2 = 8B_1$, the value of $x$ is

The flux density obtained at the centre of a circular coil of radius $R$ which carries a current $i$ is $B_0$. At a distance $pR$ from the centre on the axis,the flux density will be

$A$ wire of certain length carries a steady current. It is first bent to form a circular coil of one turn. The same wire is then bent to form a circular coil of three turns. The ratio of magnetic inductions at the centre of the coil in the two cases is

Two identical conducting wires $AOB$ and $COD$ are placed at right angles to each other. The wire $AOB$ carries an electric current $I_1$ and $COD$ carries a current $I_2$. The magnetic field at a point lying at a distance $d$ from $O$,in a direction perpendicular to the plane of the wires $AOB$ and $COD$,will be given by