Two capacitors $C_1$ and $C_2$ are are charged to $120\, V$ and $200\, V$ respectively. It is found that by connecting them together the potential on each one can be made zero . Then

Four identical capacitors are connected in series with a battery of $emf$ $10\,V$. The point $X$ is earthed, then the potential of point $A$ is.....$V$

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

Find flux related to shaded face $BCGF$

Electric potential at any point is : $V = -5x + 3y + \sqrt {15} z$ ; then the magnitude of electric field is :-

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