1. Electric Field Lines Drawing electric field lines Motion of charged particles in an electric field Electric flux

2. Electric Field Lines Electric field lines are a way of visualizing the field. Rules for Drawing field lines: 1)Lines start on (+) charges, end on (-) charges, or go to infinity 2)(# of lines)  charge 3)Lines never cross 4)Strength of field is proportional to the density of field lines Interpreting the picture: is parallel to the field line at each point.

3. Electric Field lines for an isolated Charge +Q + E – magnitude of field E E Q

4. Field lines + Area S, Where is the density of field lines greatest?

5. 2 Point Charges -2Q +Q Note: number of lines on -2Q is twice as many as on +Q

6. Quiz: -q qq Which way will the dipole start to move in the electric field? A)up B)down C)left D)right E)nowhere – there is no net force.

7. Quiz: -q qq Does this dipole feel a torque ? A)Yes - clockwise B)Yes – counter clockwise C)No D)Depends on the strength of E

8. Parallel Charged Plates ++++++++ ------- E approx. uniform, between the plates, except near the edges.

9. Electric Force Therefore we can solve for motion as easily as projectile motion!

10. Example: Uniform E 0.1m - An electron enters a uniform field of E = -200N/C j with an initial velocity of v o = 3x10 6 m/s i. Find: a) The acceleration of the electron b) The time it takes to travel through the region of the field c) The vertical displacement of the electron while in the field

11. Solution:

12. Electric Flux Electric flux is the measure of the “number of field lines passing through a surface S ” For uniform : Define: Electric Flux S Units: Nm 2 /C A is the surface area perpendicular to S, so Φ=EAcos(θ)

13. Notes: 1) is a scalar called electric flux 2)Units: Nm 2 /C 3) represents the “number of field lines through surface S.” 4)For a closed surface, the area vector points in the outward direction. 5) Flux is zero for a surface parallel to the field (normal is at 90 o to E)

14. Example: Find: flux through S 1, S 2, S 3. 30° (rectangle, 1m x 2m) (rectangle, 1m x 2m) (hemisphere, radius 1m) S2S2 S1S1 S3S3

15. solution

16. If E is not uniform, or S is not flat, then: For a small surface For the whole surface,

17. Summary Electric field lines help show the direction of E Electric flux is defined as the magnitude of the field times the area (maybe negative if the angle between the vectors is more than 90 degrees) Electric flux is a quantitative equivalent to “the number of field lines through a surface”.