The current of $5 \mathrm{~A}$ flows in a square loop of sides $1$ $\mathrm{m}$ is placed in air. The magnetic field at the centre of the loop is $\mathrm{X} \sqrt{2} \times 10^{-7} \mathrm{~T}$. The value of $\mathrm{X}$ is____.

The electric current in a circular coil of four turns produces a magnetic induction $32\,T$ at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be $..........\,T$

Three infinite wires are arranged in space in three dimensions.(along $x, y$ and $z$ axis) as shown. Each wire carries current $i$ . Find magnetic field at $A$ 

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is $1: 1$. The magnetic field at point $P$ is ...... .

Two insulated circular loop $A$ and $B$ radius ' $a$ ' carrying a current of ' $\mathrm{I}$ ' in the anti clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be :

A straight wire carrying a current of $12\; A$ is bent into a semi-circular arc of radius $2.0\; cm$ as shown in Figure $(a)$. Consider the magnetic field $B$ at the centre of the arc.

$(a)$ What is the magnetic field due to the straight segments?

$(b)$ In what way the contribution to $B$ from the semicircle differs from that of a circular loop and in what way does it resemble?

$(c)$ Would your answer be different if the wire were bent into a semi-circular arc of the same radius but in the opposite way as shown in Figure $(b)$