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During my physics lecture, the professor said that flux on a closed surface is equal to zero. What exactly is a closed surface defined as?

This problem also requires the use of the Flux = Field * Area formula. In relation to the direction of the electric field, what is the area for Part B? I'm just having trouble understanding the importance of closed surfaces vs. non-closed surfaces and how to tell them apart. Thanks

This problem also requires the use of the Flux = Field * Area formula. In relation to the direction of the electric field, what is the area for Part B? I'm just having trouble understanding the importance of closed surfaces vs. non-closed surfaces and how to tell them apart. Thanks