Electric Fields of Charge Distributions Practice Test

A charged-particle lens uses a uniformly charged disk of radius $R=0.10,\text{m}$ with surface charge density $\sigma=+4.0,\mu\text{C/m}^2$; the on-axis electric field at point $P$ a distance $z=0.050,\text{m}$ from the disk center is required to estimate focusing strength in $\text{N/C}$. The disk lies in the $y$–$z$ plane and its axis is the $x$-axis, with $P$ on $+x$. Assume vacuum and a thin disk. Consider the setup described above. Calculate the electric field at point P on the axis of the charged disk.

A shielding demo uses a uniformly charged solid insulating sphere with radius $R=0.30,\text{m}$ and volume charge density $\rho=+1.5,\mu\text{C/m}^3$; a probe at $r=0.10,\text{m}$ checks the predicted interior field. Consider the setup described above. Using Gauss’s Law, determine the electric field inside the charged sphere.