An infinitely long straight conductor is bent into a shape as shown in the figure. It carries a current $i$ amperes and the radius of the circular loop is $r$meter. Then, the magnetic induction at its center will be,

A part of a long wire carrying a current $i$ is bent into a circle of radius $r$, as shown in the figure. The net magnetic field at the Centre $O$ of the circular loop is

In the figure, what is the magnetic field at the point $O$?

The figure $\left(\mathrm{a}\right)$ shows two wires, each carrying a current. The wire $1$ consists of a circular arc of radius $R$ and two radial lengths; it carries current $i_1=2.0 \mathrm{A}$ in the direction indicated. The wire $2$ is long and straight; it carries a current $i_2$ that can be varied, and it is at a distance of $\frac{R}{2}$ from the Centre of the arc. The net magnetic field $\overrightarrow{B}$ due to the two currents is measured at the Centre of curvature of the arc. Figure $\left(\mathrm{b}\right)$ is a plot of the component of $\overrightarrow{B}$ in the direction perpendicular to the figure as a function of current $i_2$. What is the angle subtended by the arc?

A current-carrying wire loop, in fig $\left(a\right)$, lies in one plane and consists of a semicircle of radius $10.0 \mathrm{cm}$, a smaller semicircle with the same center, and two radial lengths. The smaller semicircle is rotated out of that plane by an angle $\mathrm{\theta }$ until it is perpendicular to the plane [fig (b)]. Figure $\left(c\right)$ gives the magnitude of the net magnetic field at the center of curvature versus angle $\mathrm{\theta }$. What is the radius of the smaller semicircle?

A circular coil is in $y-z$ plane with Centre at the origin. The coil is carrying a constant current. Assuming direction of the magnetic field at $x=-25 \mathrm{cm}$ to be the positive direction of the magnetic field, which of the following graphs shows the variation of the magnetic field along the $x$ axis

The magnetic field at the Centre of a circular coil of a radius $r$ is $\pi$ times that due to a long straight wire at a distance $r$ from it, for equal currents. The following figures show three cases: in all cases, the circular part has a radius $r$ and straight ones are infinitely long. For the same current, the $B$ field at the Centre $P$ in case of diagrams $1$, $2$ and $3$ has the ratio