Download B

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 B
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem B1:
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 B
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem B2:
A “semi-infinite” non-conducting rod (that is, infinite in one direction only) has uniform
linear charge density . Show that the electric field at point P makes an angle of 45⁰ with
the rod and that this result is independent of the distance R. (Hint: Separately find the
parallel and perpendicular (to the rod) components of the electric field at P, and then
compare those components.)
Lab B
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem B3:
A thin glass rod is bent into a semicircle
of radius r. A charge  q is uniformly
distributed along the upper half, and a
charge  q is uniformly distributed
along the lower half, as shown. Find the
magnitude and direction of the electric
field E at P, the center of the semicircle.
Lab B
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem B4:
A line of positive charge is formed into a
semicircle of radius R=60.0cm, as shown.
The charge per unit length along the
semicircle is described by the expression
  0 cos  , where 0 = constant. The
total charge on the semicircle is 12.0 C.
Calculate the total force on a charge of
3.00 C placed at the center of curvature.
Lab B
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem B5:
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 ), the
center of the semicircle?
c. Find the magnitude of the
electric field at point O.
Lab B
Phys222
Lab Activity 3: Electric Fields for Continuous Charge Distributions
Problem B6:
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 B