If an electron revolves around a nucleus in a circular orbit of radius $R$ with frequency $n$,then the magnetic field produced at the centre of the nucleus will be

$A$ long straight wire of circular cross-section is made of a non-magnetic material. The wire is of radius $a$. The wire carries a current $I$ which is uniformly distributed over its cross-section. The energy stored per unit length in the magnetic field contained within the wire is

$A$ non-conducting thin disc of radius $R$ rotates about its axis with an angular velocity $\omega$. The surface charge density on the disc varies with the distance $r$ from the center as $\sigma(r)=\sigma_0\left[1+\left(\frac{r}{R}\right)^\beta\right]$,where $\sigma_0$ and $\beta$ are constants. If the magnetic induction at the center is $B=\left(\frac{9}{10}\right) \mu_0 \sigma_0 \omega R$,the value of $\beta$ is

$A$ thin wire of length $l$ is carrying a constant current $i$. The wire is bent to form a circular coil. If the radius of the coil,thus formed,is $R$ and the number of turns in it is $n$,then which of the following graphs represents the variation of magnetic field induction $B$ at the centre of the coil?

Two very long straight wires are set parallel to each other. Each carries a current $I$ in the same direction and the separation between them is $2r$. The intensity of the magnetic field at point $P$ as shown in the figure is . . . . . . .

Two infinite wires carrying opposite electrical currents $I$ and $i$ are placed a distance $x$ apart. $A$ point $P$ at a distance $y$ away from the wire carrying current $i$ is shown in the figure. If the magnetic field is zero at point $P$,then the magnitude of $i$ is