If $\vec E = \frac{{{E_0}x}}{a}\hat i\,\left( {x - mt} \right)$ then flux through the shaded area of a cube is

A parallel plate capacitor is charged to a potential difference of $100\ V$ and disconnected from the source of emf. A slab of dielectric is then inserted between the plates. Which of the following three quantities change?

$(i)$ The potential difference
$(ii)$ The capacitance
$(iii)$ The charge on the plates

Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre  of the ring is 

In a particle accelerator, a current of $500 \,\mu A$ is carried by a proton beam in which each proton has a speed of $3 \times 10^7 \,m / s$. The cross-sectional area of the beam is $1.50 \,mm ^2$. The charge density in this beam (in $C / m ^3$ ) is close to

Two charges  $ + 3.2\, \times \,{10^{ - 19}}\,C$ and $ - 3.2\, \times \,{10^{ - 19}}\,C$ kept $2.4\,\mathop A\limits^o $ apart forms a dipole. If it is kept in uniform electric field of intensity $4\, \times \,{10^{5\,}}\,volt/m$ then what will be its potential energy in stable equilibrium

The plates of a parallel plate capacitor are charged up to $100\, volt$. A $2\, mm$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\, mm$. The dielectric constant of the plate is