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

In the circuit shown, a potential difference of $30\, V$ is applied across $AB$ . The potential difference between the points $M$ and $N$ is....$V$

In the figure a potential of $+1200\, V$ is given to point $A$ and point $B$ is earthed, what is the potential at the point $P$ ?......$V$

The equivalent capacitance of the system of capacitors between $A$ and $B$ as shown in the figure

A spherical shell with an inner radius $'a'$ and an outer radius $'b'$ is made of conducting material. A point charge $+Q$ is placed at the centre of the spherical shell and a total charge $-q$ is placed on the shell. Final charge distribution on the surfaces as

If the electric flux entering and leaving an enclosed surface respectively is ${\phi _1}$ and  ${\phi _2}$ the electric charge inside the surface will be