Chapter 23 Electric Field Phys 133

Electric Field New long range interaction A creates field in space changes the environment B interacts with field Phys 133

Procedure Place test charge Find force remove test charge 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

Electric Field: point charge Positive point charge Negative point charge Radial from source, depends on distance Phys 133

Electric Field (multiple charges) Net force at some point is sum of the forces due to all objects around Defined Therefore, or Phys 133

What is the electric field direction at each of the dots? Which electric field is larger, E1 or E2? 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 field Field lines Phys 133

More Vector Field and Field Lines Dipole with +/+ Vector field Field lines Phys 133

Electric Field lines Rank the electric field strength in order from largest to smallest. 1 3 2 4 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 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 Q1, Q2, Q3. 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) (i)th bit of charge P Phys 133

Strategy  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 DQ 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, q…). Express the charge DQ in terms of charge density and infinitesimal variable(s) (dz, dq…)  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. Phys 133

Problem A thin rod of length L and charge Q. Find components of the electric field vector along the dotted line. Phys 133

Problem ans Express the charge DQ in terms of charge density and infinitesimal variable(s) (dz, dq…) Express all quantities (angles, distances, etc.) in terms of coordinates. Determine the components of (Ex, Ey, …) at P due to chunk expressed in terms of variables (x, y, …r, q…). Pick a generic chunk of charge DQ. Identify, P, the place in space you want the field. Draw a picture, pick a coordinate system. x y ith P x Phys 133

Problem ans x Add up contributions, sum becomes definite integral with limits corresponding to charge. Phys 133

Problem ans y Add up contributions, sum becomes definite integral with limits corresponding to charge. Phys 133

Problem ans complete Phys 133

Problem 26.49 A plastic rod with linear charge density  is bent into a quarter circle. Find the electric field at the origin. Write expressions for x and y components of field due to a small piece at angle . Write integrals for the components of total field. Evaluate, find 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

Field of line (infinite) Points directly away, decrease with distance Phys 133

Field of hoop, along axis Phys 133

Field of disk, along axis Phys 133

Field of plane (“infinite”) perpendicular to the plane Phys 133

Plane from lots of lines (perpendicular to page) Straighten up, no distance dependence 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

Rank the electric field strength at the 5 points for the ideal capacitor 1 2 3 4 5 Phys 133

Charges in an Electric Field (due to charges; we can calculate) Charge in Electric Field (experiences a force) Phys 133

Problem 26.49 A plastic rod with charge Q = 1 mC and R = 0.1 m is bent into a quarter circle. Using your past work, find the electric field at the origin. Find the net force vector for a +1 mC charge located at the origin. Find the net force for a -3 mC charge located at the origin. Phys 133

Problem 26.52 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 Phys 133

Dipole in an Electric Field Phys 133

Phys 133