$A$ closely packed coil having $1000$ turns has an average radius of $62.8\,cm$. If the current carried by the wire of the coil is $1\,A$,the value of the magnetic field produced at the centre of the coil will be (permeability of free space $\mu_0 = 4\pi \times 10^{-7}\,T\cdot m/A$) nearly:

The magnetic induction at the centre of a current-carrying circular coil of radius $10 \, cm$ is $5\sqrt{5}$ times the magnetic induction at a point on its axis. The distance of the point from the centre of the coil (in $cm$) is

The dimensions of the ratio of magnetic flux $(\phi)$ and permeability $(\mu)$ are

$A$ long wire carries a steady current. It is bent into a coil of one turn such that the magnetic induction at the centre is $B$. If the same wire is bent to form a coil of smaller radius with $n$ turns,then the new magnetic induction $B^{\prime}$ at the centre is:

$A$ 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 $(\mu_0 = \text{permeability of free space})$:

$A$ 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: