The self-inductance of a coil having $500$ turns is $50\,mH$. The magnetic flux through the cross-sectional area of the coil when the current through it is $8\,mA$ is found to be:

An air-cored solenoid with length $20 \, cm$,area of cross-section $20 \, cm^2$,and number of turns $400$ carries a current of $2 \, A$. The current is suddenly switched off within $10^{-3} \, s$. The average back $emf$ induced across the ends of the open switch in the circuit is (ignore the variation in magnetic field near the ends of the solenoid) ........ $V$.

If in a coil,the rate of change of area is $5 \, m^2/ms$ and the current changes from $2 \, A$ to $1 \, A$ in $2 \times 10^{-3} \, s$. If the magnitude of the magnetic field is $1 \, T$,then the self-inductance of the coil is ... $H$.

An emf of $2.8 \ mV$ is induced in a rectangular loop of area $150 \ cm^2$ when the current in the loop changes from $3 \ A$ to $8 \ A$ in a time of $0.2 \ s$. Then the self-inductance of the loop is (in $\mu H$)

The current $(I)$ in an inductor is varying with time $(t)$ as shown in the figure. Which of the following graphs shows the correct variation of voltage $(V)$ with time $(t)$ in the inductor?

The length of a solenoid is $\ell$,whose windings are made of a material of density $D$ and resistivity $\rho$. The winding resistance is $R$. The inductance of the solenoid is (where $m$ = mass of winding wire,$\mu_{0}$ = permeability of free space).