A conductor lies along the $$z$$-axis at $$ - 1.5 \le z < 1.5\,m$$ and carries a fixed current of $$10.0$$ $$A$$ in $$ - {\widehat a_z}$$ direction (see figure). For a field $$\overrightarrow B = 3.0 \times {10^{ - 4}}\,{e^{ - 0.2x}}\,\,{\widehat a_y}\,\,T,$$ find the power required to move the conductor at constant speed to $$x=2.0$$ $$m$$, $$y=0$$ $$m$$ in $$5 \times {10^{ - 3}}s.$$ Assume parallel motion along the $$x$$-axis.

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 $$Hg$$)