Electrostatics 2: E-field and
Gauss’s Law
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
German Parada
Phys 222
Dr. Soeren Prell
02/04/2014
Warm-up Exercises:
1) A sphere of radius 15cm is observed to have a uniform field just outside its surface of 10
N/C pointing outwards. What can we tell about the charge magnitude and distribution
inside the sphere?
2) Two infinite lines of charge (with linear charge densities of λ1 = 2 mC/m and λ2= 1mC/m) intersects at a 45° angle. Derive an expression for the E-field on a vertical line
bisecting the 45° angle as a function of the distance away from the intersection.
3) A thin charged (-Q) hollow sphere or radius A has been placed inside a thick hollow
sphere of radius B (with B > A). Sketch the set up and draw the E-field lines
4) Two very long uniform lines of charge are parallel and are separated by 0.30 m. Each line
of charge has charge per unit length +5.20 μC/m. What magnitude of force does one line
of charge exert on a 0.05 m section of the other line of charge?
Problems:
1) Derive the expression for the E-field for an infinite sheet of charge with surface charge
density σ. How would this derivation be different if the sheet was not infinite (i.e. if it
was a square with length L?)
2) a – Calculate the E-field as a function of radial distance for an empty metallic spherical
shell with thick walls (think of an egg shell with thick sides) with a total charge of 2Q.
The outer radius of the shell is R while its inner radius is 0.75R.
b – Calculate the E-field for a similar object made out of a non-conductive material, same
dimensions and charge. You can assume the charge is uniformly distributed.
3) An infinite rectangular slab of non-conductive material (thickness 2d) has a uniform
volume charge density of ρ. Calculate the E-field as a function of the distance from the
middle of the slab.
4) An infinite line of charge (linear charge density λ) has been placed in the center inside a
neutral metallic tube with thick walls (ri and ro, inner and outer radii). Sketch a graph of
the E-field as a function of the radial distance away from the line of charge.
5) A solid non-conductive sphere with radius R has a total charge of Q, but the charge is not
uniformly distributed. Rather, the volume charge density is a function of the radial
distance from the center of the sphere. Determine the E-field inside the sphere if,
a – ρ(r) = αr
b – ρ(r) = β/r
c – ρ(r) = 2γ(1 - r/R)
With constants α, β and γ. How could you calculate those constants?
Supplemental Instruction
1060 Hixson-Lied Student Success Center  294-6624  www.si.iastate.edu
Conceptual Questions:
1) Why is it not a good idea to use a cubic Gaussian surface to calculate the E-field
generated by an infinite line of charge?
2) To calculate the E field at the point indicated by the cross, I create the Gaussian surface A
and I get a value for the field. However, a friend created the Gaussian surface B and
claimed that the E field must be zero at that point. Who is correct?
3) What would be different in the derivation of the E-field for a line of charge if such line
were not infinitely long? Can it be computed easily?