The coercivity of a small magnet where the ferromagnet gets demagnetized is $$3 \times {10^3}\,A{m^{ - 1}}.$$ The current required to be passed in a solenoid of length $$10$$ $$cm$$ and number of turns $$100,$$ so that the magnet gets demagnetized when inside the solenoid, is :

In a large building, three are $$15$$ bulbs of $$40$$ $$W$$, $$5$$ bulbs of $$100$$ $$W$$, $$5$$ fans of $$80$$ $$W$$ and $$1$$ heater of $$1$$ $$kW.$$ The voltage of electric mains is $$220$$ $$V.$$ The minimum capacity of the main fuse of the building will be:

An open glass tube is immersed in mercury in such a way that a length of $$8$$ $$cm$$ extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional $$46$$ $$cm$$. What will be length of the air column above mercury in the tube now? (Atmospheric pressure $$=76$$ $$cm$$ of $$Hg$$)

A parallel plate capacitor is made of two circular plates separated by a distance $$5$$ $$mm$$ and with a dielectric of dielectric constant $$2.2$$ between them. When the electric field in the dielectric is $$3 \times {10^4}\,V/m$$ the charge density of the positive plate will be close to: