$A$ 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 figure shows a current-carrying square loop $\text{ABCD}$ of edge length '$a$' lying in a plane. If the resistance of the $\text{ABC}$ part is $r$ and that of the $\text{ADC}$ part is $2r$,then the magnitude of the resultant magnetic field at the centre of the square loop is:

Find the magnitude of the magnetic field at point $p$ due to the semi-infinite wire shown below.

When a helium nucleus covers a circle of radius $0.8 \,m$ in $2 \,s$, find the value of magnetic field $B$ at the centre of the circle.

Two long parallel wires carrying currents $8 \,A$ and $15 \,A$ in opposite directions are placed at a distance of $7 \,cm$ from each other. $A$ point $P$ is equidistant from both the wires such that the lines joining the point to the wires are perpendicular to each other. The magnitude of the magnetic field at point $P$ is $(\sqrt{2}=1.4)$ $(\mu_0=4 \pi \times 10^{-7} \,T \cdot m/A)$.

The ratio of the magnetic field at the centre of a circular ring of radius $R$ to the magnetic field at a point on its axis at a distance $2\sqrt{2}R$ from its centre is . . . . . .