Two uniformly long charged wires with linear densities $\text{λ}$ and $3\text{λ}$ are placed along $\mathrm{X}$ and $\mathrm{Y}$ axis respectively. Determined the slope of electric field at any point on the line $\mathrm{y}=\sqrt{3}\mathrm{x}$ .

The capacity of a parallel plate condenser is $15 \mu \mathrm{F}$ when the distance between its plates is $6 \mathrm{cm}$. If the distance between the plates is reduced to $2 \mathrm{cm}$, then the capacity of this parallel plate condenser will be 

A capacitor of capacitance value 1 $\mathrm{\mu }$F is charged to 30 V and the battery is then disconnected. If the remaining circuit is connected across a 2 $\mathrm{\mu }$F capacitor, the remaining circuit is connected across a 2 $\mathrm{\mu }$F capacitor, the energy lost by the system is

In the figure shown below, the initial status of capacitors and their connection is shown. Which of the following is incorrect about this circuit?