In terms of basic units of mass $(M)$,length $(L)$,time $(T)$ and charge $(Q)$,the dimensions of magnetic permeability of vacuum $(\mu_0)$ would be

$A$ wire is first bent in the form of a circular coil of $5$ turns and the same wire is then bent in the form of another circular coil of $10$ turns. If the same current is passed in both the coils,then the ratio of the magnetic fields at their centres is

At a distance of $10\, cm$ from a long straight wire carrying current,the magnetic field is $0.04\, T$. At a distance of $40\, cm$,the magnetic field will be....$T$

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.

$A$ straight wire carrying a current of $12 \,A$ is bent into a semi-circular arc of radius $2 \,cm$ as shown in the figure. Then the magnetic field due to the straight segments at the centre of the arc is

$A$ hairpin-like shape as shown in the figure is made by bending a long current-carrying wire. What is the magnitude of the magnetic field at point $P$,which lies at the center of the semicircle?