The foldy bit isn't a solar panel. Its a sun shade. Its job is to keep the telescope out of direct sunlight and help regulate temperature. Normally, space tele

The foldy bit isn't a solar panel. Its a sun shade. Its job is to keep the telescope out of direct sunlight and help regulate temperature. Normally, space telescopes will be built like Hubble or Spitzer where the mirrors are inside a cylinder which keeps light out from all directions except where the telescope is aimed. Its also insulated to keep heat from messing with measurements. JWST's mirror is so large that they couldn't build it this way because no launcher existed at the time with a large enough payload fairing to fit it. So instead of a conventional, and otherwise superior in every other way, cylinder they came up with a clever origami folding sunshade. For comparison Hubble has a 2.4 meter main lens and JWST has a 6.5 meter lens. Its so large they couldn't reliably make it out of one element either so its actually several hexagonal elements put together. This is a popular technique for large telescopes. For power JWST just has solar panels. L2 isn't that much farther from the sun than earth is so it gets sufficient power this way. But unlike Hubble's reaction wheels JWST uses RCS thrusters to change its orientation. There are pros and cons. RCS is much more reliable than reaction wheels, a lot of satellites met a premature end because their reaction wheels stopped working. But RCS only lasts as long as you have fuel. They gave JWST enough for an estimated 10 years of operation.