Phys 133 Chapter 26 Electric Field

Phys 133 Electric Field A creates field in space changes 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 chargeNegative 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 Lines Two ways to describe the same thing Dipole with +/- Vector fieldField 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: E 1 < E 2 < E 3 = E 4 B: E 3 = E 4 < E 2 < E 1 C: E 2 = E 3 < E 4 < E 1 D: E 1 < E 4 < E 2 = E 3

Phys 133 Electric Field of a “blob”

Phys 133 Charge Density Charge 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 Q 1, Q 2, Q 3.

Phys 133 Charge Density ans Charge 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 (E x, E y, …) 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. i th Determine the components of (E x, E y, …) 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 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

Charges in an Electric Field Electric Field (due to charges; we can calculate) Charge in Electric Field (experiences a force)

Phys 133 Do Workbook & 31

Phys 133 A proton traveling at a speed of 1.0x10 6 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/m 2. How far is the proton deflected when reaching far end of capacitor? (Ans: 2.2 mm) e=1.6 x C; m p =1.67 x kg;  o =8.85 x C 2 /N-m 2 Problem 26.52

Phys 133 Dipole in an Electric Field

Phys 133