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 work done in placing a charge of $$8 \times {10^{ - 18}}$$ coulomb on a condenser of capacity $$100$$ micro-farad is

Three charges $$ - {q_1}, + {q_2}$$ and $$ - {q_3}$$ are placed as shown in the figure. The $$x$$-component of the force on $$ - {q_1}$$ is proportional to

The length of a given cylindrical wire is increased by $$100\% $$. Due to the consequent decrease in diameter the change in the resistance of the wire will be