Considering the earth as a metallic sphere so its capacitance would be nearly _____ μF. (R = 6400 km, ε₀ = 8.85 x 10^-12 SI unit)

On increasing the charge on the plates of a capacitor, _____ .

In a certain region, the electric potential at point (x, y, z) m is given by V = 5x² volt. At point (3, 2, 1) m, the electric field $\overrightarrow{E}$ = _____ .

Keeping the battery connected with a capacitor, when a dielectric is introduced to replace air between the plates of the capacitor, _____ .

Inside an uncharged spherical shell, there is a concentric conducting sphere having charge Q. The potential difference between the outer surface of the sphere and the shell is V. Now, if the shell is given a -5Q charge, what is the potential difference between these surfaces ?

Energy of a capacitor is u. Now, the battery is removed and this capacitor is joined in parallel to another uncharged identical capacitor. What will be the energy of each capacitor and the energy of system of the capacitor respectively ?

4 μF and 6 μF capacitors are joined in series and 500 V is applied between the outer plates of the system. What is the charge on each plate ?

The space between the plates of a parallel plate capacitor of 1.77 μF is filled with a material having dielectric constant = 200 and breakdown strength (dielectric strength) = 2 x 10⁶ Vm^-1. If it is capable of withstanding a potential difference of 20 V between the plates, which of the following alternatives is possible for the area A of the plate and the distance 'd' between the plates ? (ε₀ = 8.85 x 10^-12 C² N m^-2)

When 4 μF, 6 μF and 12 μF capacitors are joined in series, their equivalent capacitance is C_s and when they are joined in parallel, their equivalent capacitance is C_p, then $\frac{{\mathit{C}}_{\mathit{s}}}{{\mathit{C}}_{\mathit{p}}}$ = _____ .

When the plates of a parallel plate capacitor are charged, its potential difference become 100 V. Now, a plate of dielectric material with thickness 2 mm is introduced between them. Now, in order to keep the same potential difference as before, the distance between the plates is increased by 1.6 mm. What is the dielectric constant of the plate material which is introduced ?