Why does the radar dome on the E-3 have a white stripe down the middle?
The white strip is the metallic part which houses the electronics and serves as support structure for the antenna. The black part is basically a composite (fiberglass) shell, which covers the antenna. According to RAF:


  The radar is actually the white part of the disc, the black being there to balance and streamline the radar as it rotates


According to this page:


  Each AWACS 707 plane has two fiber glass radomes, joined by a 6 ft. (1.82 m) wide metal spine to form a 30 ft. (9.14 m) diameter radome.


This can be seen in this Northrop Grumman AN/APY-1/2 AWACS multi-mode radar inside the E-3D rotodome.



The Northrop Grumman AN/APY-1/2 AWACS multi-mode radar inside the E-3D rotodome. (Credit: Scott Carson. Twitter.). Image taken from aviation.stackexchange.com

The fiberglass shell is painted over in black as black was one color that did not require metallic particles in its paint composition (which would interfere with radar waves) as discussed in another question in aviation.stackexchange.