$A$ circular coil of radius '$r$' and number of turns '$n$' carries a current '$I$'. The magnetic fields at a small distance '$h$' along the axis of the coil $(B_a)$ and at the centre of the coil $(B_c)$ are measured. The relation between $B_c$ and $B_a$ is

$A$ current $i$ is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the centre $M$ of the loop is $\frac{\mu_{0} i}{R}$ times
$(MA=R, MB=2 R, \angle DMA=90^{\circ})$

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

$A$ straight wire of diameter $0.5\, mm$ carrying a current of $1\, A$ is replaced by another wire of $1\, mm$ diameter carrying the same current. The strength of the magnetic field at a point far away is

When an electric current is passed through a solenoid,how can we determine which end behaves as a North pole and which as a South pole? Explain.

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