A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :

A square loop of edge length $$2 \mathrm{~m}$$ carrying current of $$2 \mathrm{~A}$$ is placed with its edges parallel to the $$x$$-$$y$$ axis. A magnetic field is passing through the $$x$$-$$y$$ plane and expressed as $$\vec{B}=B_0(1+4 x) \hat{k}$$, where $$B_o=5 T$$. The net magnetic force experienced by the loop is _________ $$\mathrm{N}$$.

At the centre of a half ring of radius $$\mathrm{R}=10 \mathrm{~cm}$$ and linear charge density $$4 \mathrm{~nC} \mathrm{~m}^{-1}$$, the potential is $$x \pi \mathrm{V}$$. The value of $$x$$ is _________.