$A$ $1 \mu A$ beam of protons with a cross-sectional area of $0.5 \text{ mm}^2$ is moving with a velocity of $3 \times 10^4 \text{ m/s}$. The charge density of the beam is:

An electric current passes through a wire of non-uniform cross-section,made of a homogeneous and isotropic material. If $j_A$ and $j_B$ are the current densities and $E_A$ and $E_B$ are the electric field intensities at $A$ and $B$ respectively,then $-$

The relaxation time in conductors

There is a current of $40 \ A$ in a wire of cross-sectional area $10^{-6} \ m^2$. If the number of free electrons per $m^3$ is $10^{29}$,then the drift velocity will be:

Choose the correct option with respect to the statements $A$ and $B$:
$(A)$: When no electric field is applied across a conductor,the path of free electrons between two successive collisions in it is straight.
$(B)$: When an electric field is applied across a conductor,the drift velocity of electrons is independent of time.

In a metal, the charge carrier density is $9.1 \times 10^{28} \,m^{-3}$ and its electrical conductivity is $6.4 \times 10^7 \,S \,m^{-1}$. When an electric field of $10 \,N C^{-1}$ is applied to the metal, then the average time between two successive collisions of electrons in the metal is (Mass of electron $= 9.1 \times 10^{-31} \,kg$; charge of electron $= 1.6 \times 10^{-19} \,C$)