Question

What is the key difference between the flux formula for an open surface and a closed surface?

Options

• Open surfaces have zero flux while closed surfaces do not

• Closed surfaces require the field to be uniform

• The formulas are identical; the difference is only in how the normal is chosen

• Open surfaces use \[\Phi = \int \vec{E} \cdot d\vec{A}\] while closed surfaces use \[\Phi = \oint \vec{E} \cdot d\vec{A}\]

Answer 1

The integral notation differs: an open surface uses \[\int\] (regular integral), while a closed surface uses \[\oint\] (closed loop integral). The closed surface integral emphasizes that the integration is performed over an entire closed boundary, which is essential for applying Gauss's law.