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Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Electric Fields
for
Continuous Charge Distributions
Names:
Grade:
____________
This is a group write-up. Group size will be smaller than usual (see below)..
Notes on your report:
You have been given six problems. Follow the write-up criteria shown below. There is no need to wordprocess these problems but each problem should have separate pages, i.e., be sure to start a new page when
you start a new problem.
You may work in groups of two or three. You should hand in one report but it is not appropriate to divide
and conquer entirely. Each group member must participate in the solution of each problem. Each person
will be responsible for the final write-up of at least one problem. You must understand and be able to
reproduce the answers to all of your groups’s problems.
Write-up Criteria (Be neat and professional.)
1. Restate the problem.
2. Include a drawing of the charge distribution and the point of interest.
3. Include a sample vector diagram, showing the electric field vectors for critical dq’s.
4. Use the diagram in point 2 above to help explain any cancellations due to symmetry.
5. Set up the integrals to determine the non-zero electric field components. Show your
work/reasoning for building the integrals.
6. Solve the integrals. Box or underline your solutions.
7. Assess: is your result reasonable? Do the solutions have the correct behavior far away from the
charge?
Note: It is recommended that you use lots of scratch paper to work through the problems. However, when
you turn in a draft next week or the final version in two weeks, your work must be very clear and neat,
else I won’t be able to assist you (draft) or there will be an automatic deduction (final version). Set extra
time aside for a clean write-up, it does take some time. Think first, then commit to paper. Don’t skip steps
in your algebra: if I don’t see your work there will be a deduction.
Lab A
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem A1:
As shown in the figure, a non-conducting rod of length L has charge  q uniformly distributed along its
length.
a. What is the linear charge density of the rod?
b. What is the electric field at point P, a distance a from the end of the rod?
c. If P were very far from the rod compared to L, the rod would look like a point charge. Show that
your answer to part b reduces to the electric field of a pint charge for a
L.
Lab A
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem A2:
A thin, non-conducting rod of length l (that is, letter l, not number 1) carries a line charge (x) that varies
with distance according to (x)=Ax (in SI units) as shown in the figure. A point charge q is located a
distance l (that is, letter l, not number 1) from the end of the rod as shown.
a. What are the SI units of the constant A?
b. Find the force that the line charge exerts on q.
Lab A
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem A3:
Identical thin rods of length 2a carry equal
charges Q uniformly distributed along their
lengths. The rods lie along the x axis with their
centers separated by a distance b>2a. Show that
the magnitude of the force exerted by the left rod
on the right one is given by
 kQ 2   b2 
F   2  ln  2
2 
 4a   b  4a 
Lab A
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem A4:
A uniform positive charge per unit length 
exists along a thin non-conducting rod bent into
the shape of a segment of a circle of radius R,
subtending an angle 20 as shown in the figure.
E at the center of
curvature O. (Hint: consider the field dE due to
Find the electric field
the charge dq contained within an element of
length dl  Rd . Use symmetry considerations
in setting up the integral between
  0 to
  0 to find the total field E at O.
Lab A
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem A5:
A thin, non-conducting rod is in the shape of a
semicircle of radius R. It has a varying positive
charge per unit length  described by
  0 sin 2 , where  is defined in the
figure.
a. Sketch the charge distribution along the
semicircle.
b. What is the direction of the electric field
c.
E at point ), the center of the
semicircle?
Find the magnitude of the electric field
at point O.
Lab A
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem A6:
a.
b.
Consider a uniformly charged thin-walled right circular cylindrical shell having a total charge Q,
radius R, and height h. Determine the electric field at a point a distance d from the right side of the
cylinder as shown in the figure. (Suggestion: treat the cylinder as a collection of ring charges.)
Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly
distributed through its volume. Find the filed it creates at the same point.
Lab A