Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Electric Fields
for
Continuous Charge Distributions
Names:
Grade:
____________
This is a group write-up.
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 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 group’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 with ALL relevant
quantities. If you use symbol  in your math, it should be defined and be in the drawing.
⃗.
3. Include important dq’s , and the resulting electric field vectors 𝒅𝑬
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.
Note that A is a positive constant. 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 
 4 a   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. Find the
electric field E at the center of curvature
O. (Hint: consider the field dE due to 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 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 E at point O), the
center of the semicircle?
c. 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. 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.)
b. 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