The relationship between the electric field $E$ and the current density $J$ is given by:

The dimensional formula of mobility is . . . . . .

$A$ $1 \mu A$ 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:

Assertion: The current density $\vec J$ at any point in an ohmic resistor is in the direction of the electric field $\vec E$ at that point.
Reason: $A$ point charge when released from rest in a region having only an electrostatic field always moves along electric lines of force.

In a copper wire,each atom releases one free electron. If the diameter is $1\, mm$ and the current is $1.1\, A$,find the drift velocity. (Given: Density $\rho = 9 \times 10^{3}\, kg/m^3$,Molar mass $M = 63\, g/mol$,Avogadro number $N_A = 6.023 \times 10^{23}\, mol^{-1}$,Elementary charge $e = 1.6 \times 10^{-19}\, C$)

On increasing the temperature of a conductor,its resistance increases because