When a helium nucleus covers a circle of radius $0.8 \,m$ in $2 \,s$, find the value of magnetic field $B$ at the centre of the circle.

Two concentric circular coils $X$ and $Y$ of radii $16\; cm$ and $10\; cm$ respectively,lie in the same vertical plane containing the north to south direction. Coil $X$ has $20$ turns and carries a current of $16\; A$. Coil $Y$ has $25$ turns and carries a current of $18\; A$. The sense of the current in $X$ is anticlockwise,and clockwise in $Y$,for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

Two long parallel wires $X$ and $Y$,separated by a distance of $6 \text{ cm}$,carry currents of $5 \text{ A}$ and $4 \text{ A}$,respectively,in opposite directions as shown in the figure. The magnitude of the resultant magnetic field at point $P$,which is at a distance of $4 \text{ cm}$ from wire $Y$,is $x \times 10^{-5} \text{ T}$. The value of $x$ is . . . . . . .
Take the permeability of free space as $\mu_0 = 4\pi \times 10^{-7} \text{ SI units}$.

The magnetic induction due to an infinitely long straight wire carrying a current $i$ at a distance $r$ from the wire is given by:

When equal current is passed through two coils,equal magnetic field is produced at their centres. If the ratio of the number of turns in the coils is $8: 15$,then the ratio of their radii will be

Find the magnetic field at point $P$ in the given diagram. The wire carries a current $i$.