# Introduction to Electrodynamics

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 , which carries a uniform line charge . Check that your formula is consistent with what you would expect for the case .

**Problem 2.4**

Find the electric field a distance above the center of a square loop (side ) carrying uniform line charge .

**Problem 2.5**

Find the electric field a distance above the center of a circular loop of radius , which carries a uniform line charge .

**Problem 2.6**

Find the electric field a distance above the center of a flat circular disk of radius , which carries a uniform surface charge . What does your formula give in the limit ? Also check the case .

**Problem 2.7**

Find the electric field a distance from the center of a spherical surface of radius , which carries a uniform charge density . Treat the case (outside). Express your answers in terms of the total charge on the sphere.

**Problem 2.8**

Use your result in Problem 2.7 to find the field inside and outside a sphere of radius , which carries a uniform volume charge density . Express your answers in terms of the total charge of the sphere, . Draw a graph of as a function of the distance from the center.

**Problem 2.9**

Suppose the electric field in some region is found to be , in spherical coordinates ( is some constant).

a) FInd the charge density .

b) Find the total charge contained in a sphere of radius , centered at the origin. (Do it two different ways.)

**Problem 2.10**

A charge sits at the back corner of a cube. What is the flux of 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 , which carries a uniform surface charge density .

**Problem 2.12**

Use Gauss’s law to find the electric field inside a uniformly charged sphere (charge density ).

**Problem 2.13**

Find the electric field a distance from an infinitely long straight wire, which carries a uniform line charge .

**Problem 2.14**

Find the electric field inside a sphere which carries a charge density proportional to the distance from the origin, , for some constant .

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