1. The Electric Field Electric and Magnetic Fields are Unified!

2. Working With the Electric Field Vector Field - watch the math! Coloumb’s Law: Electric Force:

3. Coulomb Force and Electric Field: Discrete to Continuous Cases Imagine that you were feeling really positive one fine day! If 0.01% of the protons in your body migrated to your head while the corresponding electrons went to your feet – estimate the size of the force acting on your body! + + + + + + - - - - - - -- - -

4. Example... 4 m 3 m E ? -1 C +1 C Find the electric field at E X1 = (0,0)X2 = (4,0) X = (4,-3) VPython example

5. Electric Field: Discrete to Continuous Cases For a finite charge distribution: Example: find the E field due to a water molecule at a point 1 nm from the O atom, along the axis of symmetry.

6. We have to make assumptions about q 1 and q 2: q 1 = - 0.41e and q 2 = 0.82 e What do you expect the answer to be?

7. Discrete - Continuous Distributions What happens as the number of charges increases? Leads to new definition:

8. Example: Charged Ring Define an appropriate charge element “dq” We can set up the expression “formally” but may only be able to integrate under special symmetry conditions How do we handle “off-axis” calculations?

9. From Ring to Disk… Do the same calculation but this time for a uniformly charged disk. What happens if the radius of the disk becomes infinite?