$A$ cell is connected between two points of a uniformly thick circular conductor. The magnetic field at the centre of the loop will be

The magnetic field due to a current-carrying circular loop of radius $3 \ cm$ at a point on the axis at a distance of $4 \ cm$ from the centre is $54 \ \mu T$. What will be its value at the centre of the loop? (in $\mu T$)

$A$ current loop consists of two identical semicircular parts each of radius $R,$ one lying in the $x-y$ plane and the other in the $x-z$ plane. If the current in the loop is $i,$ the resultant magnetic field due to the two semicircular parts at their common centre is

Two circular coils $X$ (smaller) and $Y$ (bigger), each having a single turn, carry equal currents in the same direction and subtend the same angle at point '$O$' along the axis of the coil. The distances of the centers of coil to point '$O$' are $d$ and $(d/2)$ for coil $Y$ and $X$ respectively. The radii of coils $Y$ and $X$ are $(2r)$ and $(r)$ respectively. The magnetic induction due to the bigger coil at point '$O$' is $B_y$ and that due to smaller coil $X$ at point '$O$' is $B_x$. $(d \gg r)$ The relation between $B_x$ and $B_y$ is

At what distance from a long straight wire carrying a current of $12 \, A$ will the magnetic field be equal to $3 \times 10^{-5} \, Wb/m^2$?

Two concentric thin circular rings of radii $50 \text{ cm}$ and $40 \text{ cm}$,each carry a current of $3.5 \text{ A}$ in opposite directions. If the two rings are coplanar,the net magnetic field due to the two rings at their centre is