$A$ helium nucleus makes a full rotation in a circle of radius $0.8 \ m$ in $2 \ s$. The value of the magnetic field $B$ at the centre of the circle will be

Which of the following figures correctly depicts the direction of the magnetic field of a current-carrying coil?

$A$ symmetric star-shaped conducting wire loop carries a steady current $I$ as shown in the figure. The distance between the diametrically opposite vertices of the star is $4a$. The magnitude of the magnetic field at the center of the loop is:

An arrangement with a pair of quarter circular coils of radii $r$ and $R$ with a common centre $C$ and carrying a current $I$ is shown in the figure. The permeability of free space is $\mu_0$. The magnetic field at $C$ is

Two long parallel wires carrying currents $8 \text{ A}$ and $15 \text{ A}$ in opposite directions are placed at a distance of $7 \text{ cm}$ from each other. $A$ point $P$ is equidistant from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnetic field at $P$ is $X \times 10^{-6} \text{ T}$. Find $X$. (Given: $\sqrt{2} = 1.4, \mu_0 = 4\pi \times 10^{-7} \text{ SI unit}$)

An element $\Delta l = \Delta x \hat{i}$ is placed at the origin and carries a current $I = 10 \,A$. The magnetic field on the $y$-axis at a distance of $0.5 \,m$ from the element of length $\Delta x = 1 \,cm$ is: