Electrostatics

A parallel plate capacitor has capacitance $C_0$ in air. The space between the plates is completely filled with a dielectric of dielectric constant $K$. The new capacitance is

The electric potential as a function of $x$, $y$ is given by $V=5(x^2-y^2)$ V. The electric field at a point $(2, 3)$ m is ______ V/m.

A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha\times10^{-7}$ J. The value of $\alpha$ is ______. (combined capacitance of spheres is 200 pF)

Two metal plates $(A, B)$ are kept horizontally with separation of $\left(\frac{12}{\pi}\right)$ cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 g/cm$^3$) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials $V_A$ and $V_B$ are required on plates A and B respectively in order to ensure the droplets do not descend. The values of $V_A$ and $V_B$ are ______. (Neglect the air resistance to the droplets and take $g=10\ \mathrm{m/s^2}$)

Two point charges $8\ \mu C$ and $-2\ \mu C$ are located at $x=2$ cm and $x=4$ cm, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is ______.

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^{\alpha}$, where $\alpha$ is ______.

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\vec E_1=E_0\hat x$. If another electric field $\vec E_2=2E_0(\hat y+\hat z)$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: In electrostatics, a conductor does not store any net charge inside. Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift. Choose the correct answer from the options given below

A thin half ring of radius 35 cm is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of $Q$ is ________ nC. ($\epsilon_0=8.85\times10^{-12}\ \mathrm{C^2/Nm^2}$ and $\pi=3.14$)

A three coulomb charge moves from the point $(0,-2,-5)$ to the point $(5,1,2)$ in an electric field expressed as $\vec E=2x\hat i+3y^2\hat j+4\hat k$ N/C. The work done in moving the charge is ______ J.