A long solenoid carrying a current produces a magnetic field '$B$' along its axis. If the currunt is tripled and the number of turns per cm is halved then new value of magnetic field will be

The self inductance of an air-core inductor (solenoid) is $0.03$ mH. By introducing an iron core into inductor the self-inductance increases to $30$ mH. The relative permeability of the core used is

A coil of effective area $3$ m$^2$ is placed at right angles to a magnetic field of induction $0.05$ Wb/m$^2$. If the field is decreased to $20\%$ of its original value in $10$ second, the e.m.f. induced in the coil will be

In a series LCR circuit, the voltage across R is $100$ V, $R = 1\,\text{K}\,\Omega$ and $C = 2\,\mu\text{F}$. The angular frequency $\omega$ is $200$ rad s$^{-1}$. At resonance, the voltage across '$L$' is