An element $dl = dx \hat{i}$ (where,$dx = 1 \, cm$) is placed at the origin and carries a large current $i = 10 \, A$. What is the magnetic field on the $Y$-axis at a distance of $0.5 \, m$?

$A$ long solenoid has $100 \, \text{turns/m}$ and carries current $i$. An electron moves within the solenoid in a circle of radius $2.30 \, \text{cm}$ perpendicular to the solenoid axis. The speed of the electron is $0.046 \, c$ ($c = 3 \times 10^8 \, \text{m/s}$ is the speed of light). Find the current $i$ in the solenoid (approximate). (in $ \text{A}$)

$A$ regular polygon of $6$ sides is formed by bending a wire of length $4 \pi \text{ m}$. If an electric current of $4 \pi \sqrt{3} \text{ A}$ is flowing through the sides of the polygon,the magnetic field at the centre of the polygon would be $x \times 10^{-7} \text{ T}$. The value of $x$ is . . . . . . .

$A$ solenoid of $1000$ turns per metre has a core with relative permeability $500$. Insulated windings of the solenoid carry an electric current of $5 \, A$. The magnetic flux density produced by the solenoid is (permeability of free space $= 4 \pi \times 10^{-7} \, H/m$)

An electron $(e)$ moves in a circular orbit of radius '$r$' with uniform speed '$V$'. It produces a magnetic field '$B$' at the center of the circle. The magnetic field $B$ is ($\mu_0 =$ permeability of free space).

Two concentric thin circular rings of radii $50 \text{ cm}$ and $40 \text{ cm}$,each carry a current of $3.5 \text{ A}$ in opposite directions. If the two rings are coplanar,the net magnetic field due to the two rings at their centre is