Electric Fields II

1. Definition: Electric Fields II Electric fields are produced by point charges and continuous charge distributions is force exerted on charge by an external field Note: q produces a field but it is not external

2. B : (0,y) a a A : (x,0) x -q +q Example: Electric Dipole Derive an expression for at point B. y

3. Dipole solution:

4. For fun: find E at point A, and show that it is approximately proportional to x-3, at large distances x.

5. dq + + + + + + + + + dE + + + Source Continuous Charge Distributions E = ? • Cut source into small (“infinitesimal”) charges dq • Each produces or

6. Steps: • Draw a coordinate system on the diagram • Choose an integration variable (e.g.,x) • Draw an infinitesimal element dx • Write r and any other variables in terms of x • Write dq in terms of dx • Put limits on the integral • Do the integral or look it up in tables.

7. L d Example: Uniformly-Charged Thin Rod (length L, total charge Q) + + + + + + + + + Charge/Length = “Linear Charge Density” = constant = Q/L

8. Solution:

9. In 2D problems, integrate components separatelyto obtain the electric field: { x-component of

10. Example: Uniformly-Charged Ring y R x (x,0) Total charge Q, uniform charge/unit length, radius R Find: E at any point (x, 0)

11. Solution:

12. y R x Example: Uniformly-Charged Semicircle + + + + Charge/unit length, , is uniform Find: at origin

13. Solution:

14. Summary • Field of several point charges qi: • Field of continuous charge distribution: