The magnetic field due to a current-carrying circular loop of radius $6 \text{ cm}$ at a point on the axis at a distance of $8 \text{ cm}$ from the centre is $27 \mu \text{T}$. The magnetic field at the centre of the current-carrying loop is: (in $\mu \text{T}$)

$A$ negative charge is given to a non-conducting loop and the loop is rotated in the plane of paper about its centre as shown in the figure. The magnetic field produced by the ring affects a small magnet placed above the ring in the same plane.

$A$ current $I$ flows in an anticlockwise direction in a circular arc of a wire having $\left(\frac{3}{4}\right)^{\text{th}}$ of the circumference of a circle of radius $R$. The magnetic field $B$ at the centre of the circle is $(\mu_0 = \text{permeability of free space})$

Two infinite wires carrying opposite electrical currents $I$ and $i$ are placed a distance $x$ apart. $A$ point $P$ at a distance $y$ away from the wire carrying current $i$ is shown in the figure. If the magnetic field is zero at point $P$, then the magnitude of $i$ is

$A$ thin ring of $10 \, cm$ radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40 \pi \, rad \, s^{-1}$ about its axis,perpendicular to its plane. If the magnetic field at its centre is $3.8 \times 10^{-9} \, T$,then the charge carried by the ring is close to $\left( \mu_0 = 4 \pi \times 10^{-7} \, N/A^2 \right)$.

Write the equation for the magnetic field on the axis of a circular current-carrying loop at a distance from the center equal to its radius.