Two capacitors $C_1$ and $C_2 = 2\,C_1$ are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and $C_1$ holds charge $Q$. The switch is closed. At steady state, the charge on capacitors will be

A particle of charge $Q$ and mass $m$ travels through a potential difference $V$ from rest. The final momentum of the particle is

A parallel plate capacitor with air between the plates has a capacitance of $9\ pF$. The separation between its plates is '$d$'. The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac{2d}{3}$. Capacitance of the capacitor is now........$pF$

Assertion : The positive charge particle is placed in front of a spherical uncharged conductor. The number of lines of forces terminating on the sphere will be more than those emerging from it.

Reason : The surface charge density at a point on the sphere nearest to the point charge will be negative and maximum in magnitude compared to other points on the sphere

Two equal point charges are fixed at $x = -a$ and $x = + \,a$ on the $x$-axis. Another  point charge $Q$ is placed at the origin. The change in the electrical potential energy of $Q$ ehen it is displaced by a small distance $x$ along the $x$ -axis is apporximately proportional to

Two charges $q_1$ and $q_2$ are placed $30\,cm$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40\,cm$ from $C$ to $D$. The change in the potential energy of the $\frac{{{q_3}}}{{4\pi \,{ \in _0}}}k$ , where $k$ is