$A$ Helmholtz coil has a pair of loops,each with $N$ turns and radius $R$. They are placed coaxially at a distance $R$ apart,and the same current $I$ flows through the loops in the same direction. The magnitude of the magnetic field at $P$,the midpoint between the centers $A$ and $C$,is given by (Refer to figure):

$A$ straight conductor of length $32 \,cm$ carries a current of $30 \,A$. Magnetic induction at a point in air at a perpendicular distance of $12 \,cm$ from the mid-point of the conductor is (in $G$)

$A$ plastic disc of radius $R$ has a charge $q$ uniformly distributed over its surface. If the disc is rotated at an angular frequency $\omega$ about its axis,the magnetic induction at the center of the disc is:

Two circular coils $P$ and $Q$ of $100$ turns each have the same radius of $\pi \text{ cm}$. The currents in $P$ and $Q$ are $1 \text{ A}$ and $2 \text{ A}$ respectively. $P$ and $Q$ are placed with their planes mutually perpendicular and their centers coinciding. The resultant magnetic field induction at the center of the coils is $\sqrt{x} \text{ mT}$,where $x = \_\_\_$.
$\left[\text{Use } \mu_0 = 4\pi \times 10^{-7} \text{ T m A}^{-1}\right]$

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 a single turn. If the same current flows through the new coil,the magnetic induction at the centre will be $.......... \ T$.

In the given diagram,two current-carrying circular loops of radius $R$ and $2R$ are arranged in the $YZ-$ plane and $XZ-$ plane respectively. The common center of both is at the origin $O$. What will be the angle of the resultant magnetic field from the $X-$ axis?