Phys 133

Chapter 26

Electric Field

Phys 133

Electric Field

A creates field in spacechanges the environment

B interacts with field

New long range interaction

Phys 133

•Place test charge

•Find force

•remove test charge

Procedure

Phys 133

Simulation: Electric Field

Phys 133

Understanding Fields (in general)

Vector field worksheet (field at tail, relative lengths)

Phys 133

Vector field worksheet (cont.)

Phys 133

Vector field worksheet (ans)

Phys 133

Positive point charge

Negative point charge

Radial from source, depends on distance

Electric Field: point charge

Phys 133

Electric Field (multiple charges)Net force at some point is sum of the forces due to all objects around

Defined

or

Therefore,

Phys 133

Do workbook 26.5ac, 7adf

Phys 133

Electric field of a dipole along the y-axis…

Phys 133

Electric field of a dipole along the y-axis…

Phys 133

Electric field of a dipole along the y-axis

What is the electric field of a dipole for y >> d?

Phys 133

Vector Field and Field LinesTwo ways to describe the same thing

Dipole with +/-

Vector field Field lines

Phys 133

Dipole with +/+

Vector field Field lines

More Vector Field and Field Lines

Phys 133

Electric Field lines

Rank the electric field strength in order from largest to smallest.

A: E1 < E2 < E3 = E4

B: E3 = E4 < E2 < E1

C: E2 = E3 < E4 < E1

D: E1 < E4 < E2 = E3

Phys 133

Electric Field of a “blob”

Phys 133

Charge DensityCharge Q is spread uniformly on a rectangle of sides a and b.

a) What is the surface charge density?

b) The original rectangle, #1, is then broken into two smaller rectangles, #2 and #3. Compare the surface charge densities, 1, 2, 3. and the charges Q1, Q2, Q3.

Phys 133

Charge Density ansCharge Q is spread uniformly on a rectangle of sides a and b.

a) What is the surface charge density?

b) The original rectangle, #1, is then broken into two smaller rectangles, #2 and #3. Compare the surface charge densities, 1, 2, 3.

Charge is uniformly spread over rectangle.Piece #2 has a 1/3 the area, so 1/3 the charge.

Phys 133

Electric Field (continuous distribution)

P

(i)th bit of charge

Phys 133

Draw a picture, pick a coordinate system.

Identify, P, the place in space you want the field. Pick a generic (no special points) chunk of charge Q for

which you know the field.

Determine the components of (Ex, Ey, …) at P due to chunk expressed in terms of variables (x, y, …r, …).

Express the charge Q in terms of charge density and infinitesimal variable(s) (dz, d…)

Express all quantities (angles, distances, etc.) in terms of coordinates.

Add up contributions, sum becomes definite integral with limits corresponding to charge.

Evaluate integral and simplify result as much as possible.

Strategy

Phys 133

A thin rod of length L and charge Q. Find components of the electric field vector along the dotted line.

Problem

Phys 133

Problem ans

x

y

Draw a picture, pick a coordinate system.Identify, P, the place in space you want the field.Pick a generic chunk of charge Q.

ith

Determine the components of (Ex, Ey, …) at P due to chunk expressed in terms of variables (x, y, …r, …).

P

Express the charge Q in terms of charge density and infinitesimal variable(s) (dz, d…)Express all quantities (angles, distances, etc.) in terms of coordinates.

x

Phys 133

Add up contributions, sum becomes definite integral with limits corresponding to charge.

Problem ans x

Phys 133

Add up contributions, sum becomes definite integral with limits corresponding to charge.

Problem ans y

Phys 133

Problem ans complete

Phys 133

A plastic rod with linear charge density is bent into a quarter circle. Find the electric field at the origin.

a) Write expressions for x and y components of field due to a small piece at angle .

b) Write integrals for the components of total field.

c) Evaluate, find

Problem 26.49

Phys 133

Problem 26.49 ans

(i)th bit of charge

Phys 133

Field of quarter circle of charge

Phys 133

Other charge geometries

• Line

• Hoop

• Disk (from hoops)

• Plane (from disk)

Phys 133

Points directly away, decrease with distance

Field of line (infinite)

Phys 133

Field of hoop, along axis

Phys 133

Field of disk, along axis

Phys 133

perpendicular to the plane

Field of plane (“infinite”)

Phys 133

Straighten up, no distance dependence

Plane from lots of lines (perpendicular to page)

Phys 133

Parallel-plate Capacitor•Net charge is zero

•Charge lost from +Q side ends up on -Q side

Phys 133

Find the electric field inside capacitor

Phys 133

Phys 133

Charges in an Electric Field

Electric Field (due to charges; we can calculate)

Charge in Electric Field(experiences a force)

Phys 133

Do Workbook 26.28 & 31

Phys 133

A proton traveling at a speed of 1.0x106 m/s enters the gap between the plates of a 2.0-cm wide parallel plate capacitor. The plates have a surface charge density of +/- 1.0x10-6 C/m2. How far is the proton deflected when reaching far end of capacitor?

(Ans: 2.2 mm)

e=1.6 x 10-19C; mp=1.67 x 10-27kg; o=8.85 x10-12C2/N-m2

Problem 26.52

Phys 133

Dipole in an Electric Field

Phys 133