Magnitude of magnetic field (in $SI$ units) at the centre of a hexagonal shape coil of side $10\, cm$, $50$ turns and carrying current $I$ (Ampere) in units of $\frac{\mu_{0} I}{\pi}$ is

Magnetic field due to a ring having $n$ turns at a distance $x$ on its axis is proportional to (if $r$ = radius of ring)

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 it axis, the induction at the center of the disc is :-

Two very thin metallic wires placed along $X$ and $Y$-axis carry equal currents as shown here. $AB$ and $CD$ are lines at $45^\circ $ with the axes with origin of axes at $O$. The magnetic field will be zero on the line

A current of $0.1\, A$ circulates around a coil of $100$ $turns$ and having a radius equal to $5\,cm$. The magnetic field set up at the centre of the coil is ($\mu_0 = 4\pi \times 10^{-7} weber/amp-metre$)

A vertical wire kept in $Z-X$ plane carries a current from $Q$ to $P$ (see figure). The magnetic field due to current will have the direction at the origin $O$ along