Depends on how you enclose it - and if the magical barrier does reflect light under extreme angles.
Encased in glass
Let's assume someone uses a glass bubble to enclose the atmosphere. Then we are suddenly sitting in a ginormous greenhouse, as light reflected from the clouds would hit the glass at an extreme angle, getting reflected back to the clouds.
As a result, Earth would increase the reflection to earth and thus heat absorption, reducing the overall albedo by up to 3/4. That means it would get hot:
Of the 1400 W/m² reaching earth, the loss wouldn't be ca. 400 W/m² from albedo but more like 100 W/m², so about 30% more energy would get deposited to earth as thermal energy. That'd bring up earth's temperature slowly but surely, within a couple of months to years. It would be a rather humid but hot planet, with the ice poles melting, for some years, and on an order of decades, turn the inland of the continents into deserts. Think about all the world being like Australia but for the fact that not every animal wants to kill you.
Encased in tinfoil
If you want to be really nasty, take tinfoil with a mirror sheen. The albedo of that is in the area of 98%. As a result, of the 1400 W/m² sunlight reaching earth and of which usually roundabout 1000 W/m² keep it warm and habitable, suddenly only 20 to 30 W/m² do that directly, and the light emitted from the heated foil would be minimal. Earth gets rather cold and also totally dark. It's worse than nuclear winter! The winter will come within hours to days, leaving not a single living thing.
Encased in cellophane
Cellophane would behave like the glass house.
Non climate effects
Besides the climate getting devastated, there'd be a radical effect on the satellite networks: 2018 saw 111 successful launches of satellites and probes. Of them we have 23 Navigation, 47 Communication satellites, 5 Meteorological and 77 Earth Observation sattelites. Most sattelites are launched to complete systems or replace old satellites that have failed - without the ability to launch new satellites, our satellite systems would soon fail. The resultes on a society level are huge:
- GPS and similar systems would fail within about 5 to 10 years.
- TV satellite broadcast would follow in the same time frame.
- Satellite telephone follows in suite.
- ca. 3 to 15 people get stranded on the ISS, forced to starve to death. Once the field opens again, the station has evolved into a huge biohazard, the bacteria and mold in it very likely changed a lot.