The magnetic field at the origin due to the current $I$ flowing in the wire is -

Write the equation for the magnetic field of a current-carrying circular loop at: $(i)$ a point on the axis,and $(ii)$ a point on the plane of the loop at a distance $x$ from the center of the loop.

Two circular coils $P$ and $Q$ of $100$ turns each have the same radius of $\pi \text{ cm}$. The currents in $P$ and $Q$ are $1 \text{ A}$ and $2 \text{ A}$ respectively. $P$ and $Q$ are placed with their planes mutually perpendicular and their centers coinciding. The resultant magnetic field induction at the center of the coils is $\sqrt{x} \text{ mT}$,where $x = \_\_\_$.
$\left[\text{Use } \mu_0 = 4\pi \times 10^{-7} \text{ T m A}^{-1}\right]$

$A$ 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:

$A$ circular coil of wire consisting of $n$ turns,each of radius $8 \ cm$,carries a current of $0.4 \ A$. The magnitude of the magnetic field at the centre of the coil is $3.14 \times 10^{-4} \ T$. The value of $n$ is (Take $\mu_0 = 12.56 \times 10^{-7} \ T \cdot m/A$)

The Earth's magnetic field at a given point is $0.5 \times 10^{-5} \, Wb/m^2$. This field is to be annulled by the magnetic induction at the center of a circular conducting loop of radius $5.0 \, cm$. The current required to be flown in the loop is nearly......$A$