Lecture 3Today’s topics:

1. Finish the two charge problem

2. ! of an electric dipole

3. ! of a uniformly charged line segment

4. Other electric fields (ring, disk, infinite plane)

5. Motion of a charge in a uniform !.

6. Dipole in a uniform ! (force, torque, potential energy)

7. Dipole in a Coulomb field

See a video of prof. Tom Hemmick solving this problem: https://www.youtube.com/watch?v=diDRJsfxkVw&list=PLFC-adHQMw33THYSrlDC0KvwVJ99FyLSW

!",$ = !" cos )" =!" $*+$,-,= . /,-,0 (23−2") = 878. 9.:",

!",; = !" sin )" =!" ;*+;,-,= . /,-,0 (>3−>") = 878. :.:", Beware of signs! Get them from the picture!

-

- -

!"#,% = +!" sin+ = !" ,- ,

!".,% = −!" sin+ = −!" ,- ,

- = 0# + ,#

Summarizing:For a disk in the x,y plane, centered at 0, with radius R, the ! field along the +z axis is:! " = $

%&'1 − *

*+ ,-./0, where /0 is the unit vector along the z axis, 1 =

Remember what is 23? Coulomb’s constant 0 = *45&'

. If we take 6 ≫ ", the denominator of the second term is very large -> second term goes to 0.! " = $

%&'/0, independent on z! This is a constant (uniform) field along the +z axis.

If we are below the disk, ! " = − $%&'

/0 (also uniform).In both cases (+z, -z), the field points away from the positively charged disk.