The direction of magnetic lines of force close to a straight conductor carrying current will be

Charge $q$ is uniformly spread on a thin ring of radius $R.$ The ring rotates about its axis with a uniform frequency $f \ Hz.$ The magnitude of magnetic induction at the center of the ring is

Two identical long current-carrying wires are bent into the shapes shown in the following figures. If the magnitudes of the magnetic fields at the centers $P$ and $Q$ of the semicircular arcs are $B_1$ and $B_2$ respectively,then the ratio $\frac{B_1}{B_2}$ is . . . . . . .

$A$ coil having $100$ turns is wound tightly in the form of a spiral with inner and outer radii $1 \text{ cm}$ and $2 \text{ cm}$,respectively. When a current $1 \text{ A}$ passes through the coil,the magnetic field at the centre of the coil is

$A$ current $I$ flows in a circular arc of radius $r$ subtending an angle $\theta$ at the centre $O$ as shown in the figure. Find the magnetic field at the centre $O$ of the circle.

Figures $A$ and $B$ show two long straight wires of circular cross-section (radii $a$ and $b$ with $a < b$),each carrying a current $I$ which is uniformly distributed across the cross-section. The magnitude of the magnetic field $B$ varies with radial distance $r$ from the axis. Which of the following graphs correctly represents the variation of $B$ with $r$ for both wires?