Electrostatic P...

Two parallel plate capacitors of capacitances $$C$$ and $$2C$$ are connected in parallel and charged to a potential difference $$V$$. The battery is then disconnected and the region between the plates of the capacitor $$C$$ is completely filled with a material of dielectric constant $$K$$. The potential difference across the capacitors now becomes :

A series combination of $$n_1$$ capacitors, each of value $$C_1$$, is charged by a source of potential difference 4 V. When another parallel combination of $$n_2$$ capacitors, each of value $$C_2$$, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of $$C_2$$, in terms of $$C_1$$, is then

A parallel plate capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given by $$Q_0, V_0, E_0$$, and $$U_0$$ respectively. A dielectric slab is now introduced to fill the space between the plates with the battery still in connection. The corresponding quantities now given by $$Q, V, E$$ and $$U$$ are related to the previous ones are :

The equivalent capacitance between x and y is :

Find equivalent capacitance between points A and B :
[Assume each conducting plate is having same dimensions and neglect the thickness of the plate, $$\dfrac {\varepsilon_0A}{d}=7\mu F$$, where A is area of plates]

Figure shows a parallel plate capacitor with plate area $$A$$ and plate separation $$d$$. A potential difference is being applied between the plates. The battery is then disconnected and a dielectric slab of dielectric constant $$K$$ is placed in between the plates of the capacitor as shown.
Now, answer the following questions based on above information. The electric field in the gaps between the plates and the dielectric slab will is :

A parallel plate capacitor of plate area $$A$$ and plate separation $$d$$ is charged to potential difference $$V$$ and then the battery is disconnected. A slab of dielectric constant $$K$$ is then inserted between the plates of capacitor so as to fill the space between the plates. If $$Q, E$$ and $$W$$ denote respectively, the magnitude of charge on each plate electric field between the plates (after the slab is inserted), and work done on the system, in question, in the process of inserting the slab, then which is wrong?

Positive charge Q is uniformly distributed throughout the volume of a dielectric sphere of radius R. A point mass having charge +q and mass m is fired towards the centre of the sphere with velocity v from a point A at distance r(r> R) from the centre of the sphere. Find the minimum velocity v so that it can penetrate R/2 distance of the sphere. Neglect any resistance other than electric interaction. Charge on the small mass remains constant throughout the motion.

A parallel plate capacitor of area A and separation $$d$$ is charged to potential difference $$V$$ and removed from the charging source A dielectric slab of constant $$K = 5$$, thickness $$d$$ and area $$\displaystyle \frac{A}{3}$$ is inserted as shown in the figure Let $$\displaystyle \sigma _{1}$$ be free charge density at the conductor-dielectric surface and $$\displaystyle \sigma _{2}$$ be the charge density at the conductor-vacuum surface :

Which list below places the capacitors in order of increasing capacitance ?