# Old

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I found some old notes of mine that are solutions to problems found in Griffith’s Electrodynamics and I’ve decided to post them here. My mistakes are included, but I think including them will be instructive for the future student who wishes to avoid the same pitfalls. Note: Corrections are in green.

Problem 2.3
Find the electric field a distance z above one end of a straight line segment of length $L$, which carries a uniform line charge $\lambda$. Check that your formula is consistent with what you would expect for the case $z \gg L$. Problem 2.4
Find the electric field a distance $z$ above the center of a square loop (side $a$) carrying uniform line charge $\lambda$. Problem 2.5
Find the electric field a distance $z$ above the center of a circular loop of radius $r$, which carries a uniform line charge $\lambda$. Problem 2.6
Find the electric field a distance $z$ above the center of a flat circular disk of radius $R$, which carries a uniform surface charge $\sigma$. What does your formula give in the limit $R \rightarrow \infty$? Also check the case $z \gg R$. Problem 2.7
Find the electric field a distance $z$ from the center of a spherical surface of radius $R$, which carries a uniform charge density $\sigma$. Treat the case $zR$ (outside). Express your answers in terms of the total charge $q$ on the sphere.  Problem 2.8
Use your result in Problem 2.7 to find the field inside and outside a sphere of radius $R$, which carries a uniform volume charge density $\rho$. Express your answers in terms of the total charge of the sphere, $q$. Draw a graph of $|\vec{E}|$ as a function of the distance from the center. Problem 2.9
Suppose the electric field in some region is found to be $\vec{E}=kr^3\hat{r}$, in spherical coordinates ( $k$ is some constant).
a) FInd the charge density $\rho$.
b) Find the total charge contained in a sphere of radius $R$, centered at the origin. (Do it two different ways.) Problem 2.10
A charge $q$ sits at the back corner of a cube. What is the flux of $\vec{E}$ through the shaded side?

Problem 2.11
Use Gauss’s law to find the electric field inside and outside of a spherical shell of radius $R$, which carries a uniform surface charge density $\sigma$. Problem 2.12
Use Gauss’s law to find the electric field inside a uniformly charged sphere (charge density $\rho$).

Problem 2.13
Find the electric field a distance $s$ from an infinitely long straight wire, which carries a uniform line charge $\lambda$.

Problem 2.14
Find the electric field inside a sphere which carries a charge density proportional to the distance from the origin, $\rho=kr$, for some constant $k$. 