Introduction to Electrodynamics

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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 .

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Problem 2.4
Find the electric field a distance z  above the center of a square loop (side a ) carrying uniform line charge \lambda .

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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 .

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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 .

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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.

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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.

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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.)

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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 .

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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 .

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