In a toroid,the number of turns per unit length is $1000$ and the current through it is $\frac{1}{4 \pi} \ A$. The magnetic field produced inside (in $Wb/m^2$) will be:

Choose the wrong statement to complete: An ideal solenoid has

$A$ long straight wire with a circular cross-section having radius $R$ is carrying a steady current $I$. The current $I$ is uniformly distributed across this cross-section. Then the variation of magnetic field due to current $I$ with distance $r$ $(r < R)$ from its centre will be:

Consider two idealized systems: $(i)$ a parallel plate capacitor with large plates and small separation,and $(ii)$ a long solenoid of length $L \gg R$,where $R$ is the radius of the cross-section. In $(i)$,$E$ is ideally treated as a constant between the plates and zero outside. In $(ii)$,the magnetic field is constant inside the solenoid and zero outside. These idealized assumptions,however,contradict fundamental laws as follows:

$A$ long solenoid is fabricated by closely winding a wire of radius $0.5 \, mm$ over a cylindrical frame so that the successive turns nearly touch each other. What is the magnetic field at the centre of the solenoid if it carries a current of $5 \, A$?

$A$ current $i$ ampere flows along the inner conductor of a coaxial cable and returns along the outer conductor of the cable. The magnetic induction at any point outside the conductor at a distance $r$ metre from the axis is