$A$ solenoid of length $0.25 \ m$ has a radius of $1 \ cm$ and is made up of $500$ turns. It carries a current of $2.5 \ A$. What is the magnitude of the magnetic field inside the solenoid? (Take $\mu_0 = 4 \pi \times 10^{-7} \ SI$ units).

The current required to be passed through a solenoid of $15\,cm$ length and $60$ turns in order to demagnetize a bar magnet of magnetic intensity $2.4 \times 10^3\,A/m$ is $.........A$.

The magnetic field intensity $H$ at the centre of a long solenoid having $n$ turns per unit length and carrying a current $I$,when no material is kept in it,is

$A$ particle of mass $2.2 \times 10^{-30} \,kg$ and charge $1.6 \times 10^{-19} \,C$ is moving at a speed of $10 \,km/s$ in a circular path of radius $2.8 \,cm$ inside a solenoid. The solenoid has $25 \,turns/cm$ and its magnetic field is perpendicular to the plane of the particle's path. The current in the solenoid is (Take $\mu_0 = 4\pi \times 10^{-7} \,H/m$) (in $\,mA$)

$A$ solenoid is $1.0 \ m$ long and it has $4250$ turns. If a current of $5.0 \ A$ is flowing through it, what is the magnetic field at its centre? $[\mu_0 = 4\pi \times 10^{-7} \ T \cdot m/A]$

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: