Physics Electrostatic Potential and Capacitance

Four identical rectangular plates with length, l = 2cm and breadth, b = 3/2 cm are arranged as shown in figure. The equivalent capacitance between A and C is xε₀A/d. The value of x is ----------. (Round off to the nearest integer)

A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12V between its plates. The charging battery is now disconnected and a porcelain plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of . pJ. (Assume no friction)

Two capacitors of capacitances C and 2C are charged to potential differences V and 2 V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:

A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height h (see figure), then: (assume the remaining portion to be spherical)

A particle of charge q and mass m is subjected to an electric field E = E₀(1 − ax²) in the x-direction, where a and E₀ are constants. Initially the particle was at rest at x = 0. Other then the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

Two identical electric point dipoles have dipole moments p₁ = pî and p₂ = −pî and are held on the x axis at distance ' a ' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is:

A capacitor C is fully charged with voltage V?. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance C/2. The energy loss in the process after the charge is distributed between the two capacitor is: