Two coils $P$ and $Q$ each of radius $R$ carry currents $I$ and $\sqrt{8} I$ respectively in the same direction. These coils are lying in perpendicular planes such that they have a common centre. The magnitude of the magnetic field at the common centre of the two coils is ($\mu_0 =$ permeability of free space).

$A$ circular coil carrying current $I$ has a radius $R$ and magnetic field at the centre is $B$. The distance from the centre along the axis of the same coil where the magnetic field will be $\frac{B}{8}$ is

$A$ coil having $N$ turns is wound tightly in the form of a spiral with inner and outer radii $a$ and $b$ respectively. Find the magnetic field at the centre,when a current $I$ passes through the coil.

Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper,as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

Two concentric coils of $20$ turns each are placed in the same plane. Their radii are $30 \text{ cm}$ and $60 \text{ cm}$,and they carry $0.4 \text{ A}$ and $0.6 \text{ A}$ currents,respectively,in opposite directions. The magnetic induction at the centre in tesla is ....... .

Two infinitely long straight wires lie in the $xy$-plane along the lines $x=+R$ and $x=-R$. The wire located at $x=+R$ carries a constant current $I_1$ and the wire located at $x=-R$ carries a constant current $I_2$. A circular loop of radius $R$ is suspended with its centre at $(0,0, \sqrt{3} R)$ and in a plane parallel to the $xy$-plane. This loop carries a constant current $I$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $+\hat{j}$ direction. Which of the following statements regarding the magnetic field $\vec{B}$ is (are) true?
$(A)$ If $I_1=I_2$, then $\vec{B}$ cannot be equal to zero at the origin $(0,0,0)$.
$(B)$ If $I_1 > 0$ and $I_2 < 0$, then $\vec{B}$ can be equal to zero at the origin $(0,0,0)$.
$(C)$ If $I_1 < 0$ and $I_2 > 0$, then $\vec{B}$ can be equal to zero at the origin $(0,0,0)$.
$(D)$ If $I_1=I_2$, then the $z$-component of the magnetic field at the centre of the loop is $\left(-\frac{\mu_0 I}{2 R}\right)$.