Phys 133 Chapter 26 Electric Field. Phys 133 Electric Field A creates field in space changes the...
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Transcript of Phys 133 Chapter 26 Electric Field. Phys 133 Electric Field A creates field in space changes the...
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