A solenoid is connected to a battery so that a steady current flows through. If an iron core is inserted into the solenoid, will the current increase or decrease? Explain.

Consider a metal ring kept on top of a fixed solenoid (say on a cardboard) (figure). The centre of the ring coincides with the axis of the solenoid. If the current is suddenly switched on, the metal ring jumps up. Explain

Consider a metal ring kept (supported by a cardboard) on top of a fixed solenoid carrying a current $\mathrm{I}$ (see Figure). The centre of the ring coincides with the axis of the solenoid. If the current in the solenoid is switched off. What will happen to the ring?

A magnetic field in a certain region is given by $B=B_0\cos \left(\omega t\right)\hat{k}$ and a coil of radius $a$ with resistance $R$ is placed in the $x-y$ plane with its centre at the origin in the magnetic field (see Figure). Find the magnitude and the direction of the current at $(a,0,0)$ at

$t=\frac{\mathrm{\pi }}{2\omega }, t=\frac{\mathrm{\pi }}{\omega }$ and $t=\frac{3\mathrm{\pi }}{2\omega }$

Consider a closed loop $\mathrm{C}$ in a magnetic Held (Figure). The flux passing through the loop is defined by choosing a surface whose edge coincides with the loop and using the formula $\Phi =B_1.d{A}_1+B_2.d{A}_2+...$ Now if we chose two different surfaces ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ having $\mathrm{C}$ as their edge, would we get the same answer for flux. Justify your answer.

Find the current in the wire for the configuration shown in Figure. Wire $\mathrm{PQ}$ has negligible resistance. $\overline{B}$, the magnetic field is coming out of the paper. $\theta$ is a fixed angle made by $\mathrm{PQ}$ travelling smoothly over two conducting parallel wires separated by a distance $d$ 

A (current vs time) graph of the current passing through a solenoid is shown in Figure. For which time is the back electromotive force $\left(u\right)$ a maximum. If the back e.m.f. at $t=3\mathrm{s}$ is $e$. find the back e.m.f. at $t=7\mathrm{s}, 15\mathrm{s}$ and $40\mathrm{s}$. $\mathrm{OA}, \mathrm{AB}$ and $\mathrm{BC}$ are straight line segments.