Electric Fields of Charge Distribution

Electrons on an insulator (zoomed in).

Zoomed out – difficult to “see” individual electrons smooth distribution of charge. Like charge is “smeared” on the insulator

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Negative…

where integral is over the entire distribution. Can also write:

Different Distributions

linear charge density, :

surface charge density,

volume charge density,

Small charge

Charge density

Small length

Small area

Small volume

Solution Process for , p.6721) Visualize the electric field from the

distribution and/or individual charges. Note any symmetries.

2) Categorize: individual charges or distribution?3) Analyze:

a) Individual charges – sum.b) Distribution – integral (see table: Appendix B,

Page A-18.)

4) Check: does the result match with your visualization at the beginning? Is it symmetric in ways that it should be?

All charged rods have the same length and the same linear charge density (+ or -). Light rods are positively charged, and dark rods are negatively charged. For which arrangement below would the magnitude of the electric field at the origin be largest?

1. {image}2. {image}3. {image}4. {image}5. {image}6. {image}7. {image}8. Impossible to determine.

1. 2. 3.

4. 5. 6.

7. 8.

Impossible to determine

Electric Field Lines

Helpful for visualizing electric fields.

In the same direction as at each point in space.

Direction of force on a positive test charge placed there direction of acceleration for positive charge.

Where does the negatively charged triangle go?

Rules for Sketching

1. Lines begin on positive charges and terminate on negative charges– If more of one type of charge, some lines will

begin or end infinitely far away.

2. The number of lines leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge.

3. No two field lines can cross.

May be helpful as you practice this:

http://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html

Two uniformly charged rods are positioned horizontally as shown. The top rod is positively charged and the bottom rod is negatively charged. The total electric field at the origin:

1. is zero. 2. has both a non-zero x component

and a non-zero y component. 3. points totally in the +x direction. 4. points totally in the –x direction. 5. points totally in the +y direction 6. points totally in the –y direction. 7. points in a direction impossible to

determine without doing a lot of math.

Rank the magnitudes of the electric field at points A, B, and C shown in the figure(greatest magnitude first).

1. A, B, C2. C, A, B3. B, C, A4. C, B, A5. A, C, B6. B, A, C

Motion of a Charged ParticleNewton’s 2nd Law:

If is “uniform” (read: constant throughout space) kinematics.

Example: A uniformly charged rod of length L and total charge Q lies along the x axis as shown in the figure. (a) Find the components of the electric field at the point P on the y axis a distance d from the origin. (b) What are the approximate values of the field components when d >> L? Explain why you would expect these results.

x

yP

d

L

Quantitative Question:You are helping to design a new electron microscope to investigate the structure of the HIV virus. A new device to position the electron beam consists of a charged circle of conductor. This circle is divided into two half circles separated by a thin insulator so that half of the circle can be charged positively and half can be charged negatively. The electron beam will go through the center of the circle. To complete the design your job is to calculate the electric field in the center of the circle as a function of the amount of positive charge on the half circle, the amount of negative charge on the half circle, and the radius of the circle.

Lab: None

Start on homework:

P37, P42, P43, P46 from Chapter 23