[2013EM/HMW-03]

PHY 102: Introduction to Physics-2
Tutorial-3
(Coulomb’s law and Gauss’s law)

1. Electric field: Continuous charge distribution. Find the electric field a distance $z$ above the center of a flat circular disk of radius $R$ (Fig.1), which carries uniform surfaces charge $\sigma$. what does your formula give in the limit $R\rightarrow \infty$? Also check the case $z\gg R$. 
2. Gauss's Law: Show that, for each of these cases (a sphere, cylinder or a slab of uniform charge density), the electric field $E(r<R)$ inside the charge distribution is given in terms of the field $E(R)$ at the boundar of the charge distribution by $\vec{E}(r<R)=\left({r\over R}\right)\vec{E}(R)$.
3. Electric field in a coaxial cable:  A long co-axial cable (Fig.2) carries a uniform volume charge density $\rho$ on the inner cylinder (radius $a$), and a uniform surface charge density on the outer cylinder shell (radius $b$).  

   This surface charge is negative and of jus the rightmagnitude so that the cable as a whole is electrically neutral. Findthe electric field in each of the three region: (i) inside the innercylinder ($s<a$), (ii) Between the cylinders ($a<s<b$), (iii)outside the cable ($s>b$). Plot $|\vec{E}|$ as a function of $s$.