$A$ long solenoid of length $L$ has a mean diameter $D$. It has $n$ layers of winding of $N$ turns each. If it carries a current $I$,the magnetic field at its centre will be

The region inside a current-carrying toroid is filled with a material (Niobium) having magnetic susceptibility $\chi = 2.6 \times 10^{-5}$. The percentage increase in the magnetic field in the presence of Niobium over that without it is:

Which of the following statements is incorrect for a current-carrying solenoid?

$A$ current of $1/4\pi \ A$ is flowing through a toroid. It has $1000$ turns per meter. The value of the magnetic field (in $Wb/m^2$) along its axis is:

The magnetic flux near the axis and inside the air core solenoid of length $60$ cm carrying current $I$ is $\frac{\pi}{2} \times 10^{-6} \text{ Wb}$. Its magnetic moment will be (cross-sectional area is very small as compared to length of solenoid, $\mu_0 = 4\pi \times 10^{-7} \text{ SI unit}$) (in $\text{ Am}^2$)

$A$ long,straight wire of radius $a$ carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance $\frac{a}{3}$ and $2a$ respectively from the axis of the wire is