A thin spherical conducting shell of radius $$R$$ has a charge $$q.$$ Another charge $$Q$$ is placed at the center of the shell. The electrostatic potential at a point $$P$$ a distance $${R \over 2}$$ from the center of the shell is

The thermo $$e.m.f.$$ of a thermo -couple is $$25$$ $$\mu V/{}^ \circ C$$ at room temperature. A galvanometer of $$40$$ $$ohm$$ resistance, capable of detecting current as low as $${10^{ - 5}}\,A,$$ is connected with the thermo couple. The smallest temperature difference that can be detected by this system is

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor

Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their usual meaning, are