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A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is

Asked in JEE Main 11th April 2nd Shift 2023 · Capacitance of a conductor and a capacitor

• (1) Zero
• (2) (CV)/(ε₀)
• (3) (CV)/(2ε₀)
• (4) (2CV)/(ε₀)

Step-by-step solution

Why the other options are wrong

• (1) Would be right only if the surface enclosed BOTH plates, whose charges +CV and -CV cancel; here only the positive plate is inside.
• (3) Halves the enclosed charge, probably by using the field σ/(2ε₀) of one plate instead of Gauss's law on the enclosed charge.
• (4) Counts the charge on both plates as +CV each and adds them, ignoring that the second plate carries -CV and is outside the surface anyway.

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