Two identical parallel plate capacitor are placed in series and connected to a constant voltage source of $V_0\, volt$. If one of the capacitors is completely immersed in a liquid with dielectric constant $K$, the potential difference between the plates of the other capacitor will change to
$\left( {\frac{{K + 1}}{K}} \right){V_0}$
$\left( {\frac{K}{{K + 1}}} \right){V_0}$
$\left( {\frac{{K + 1}}{2K}} \right){V_0}$
$\left( {\frac{2K}{{K + 1}}} \right){V_0}$
Three point charges $+q, -2q$ and $+q$ are placed at points $(x = 0, y = a, z = 0), (x = 0, y = 0,z = 0)$ and $(x = a, y = 0, z = 0)$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are
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
Four capacitors of capacitance $10\, \mu\, F$ and a battery of $200\,V$ are arranged as shown. How much charge will flow through $AB$ after the switch $S$ is closed?
There is a square gaussian surface placed in $y-z$ plane. Its axis is along $x-$ axis and centre is at origin. Two identical charges, each $Q$, are placed at point $(a, 0, 0)$ and $(-a, 0, 0)$. Each side length of square is $2a$ then electric flux passing through the square is
A thin square plate is placed in $x-y$ plane as shown in fig. such that is centre coinsides with origine it's charge density at point $(x, y)$ is $\sigma = \sigma _0xy$ (where $\sigma _0$ is constant). Find total charge on the plate.