Question

In a Van de Graaff electrostatic generator a rubber belt of 0.3 m width travels at a velocity of 20m/s. The belt is given a uniform surface charge at lower roller, so it produces a field of ${10}^{6}V/m$ in its vicinity. Current (in milliamperes) carried by the belt is

Answer 1

$E=\frac{\delta }{2{\epsilon }_0}$ , where $\delta$ is the charge density of the belt.
$\Rightarrow \delta =2E{\epsilon }_0$
$i=\frac{\Delta Q}{\Delta t}=\frac{\delta A}{\Delta t}=\frac{2E{\epsilon }_{0}A}{\Delta t}$
$i=2\times {10}^6\times 8.8\times {10}^{-12}\times 0.3\times 20$
$i=105.6\times {10}^{-6}\approx 0.1056\times {10}^{-3}$