Gauss's law and electric flux in 3D

Direct answer

Move charges in and out of a 3D Gaussian sphere or cube and watch the total flux follow Φ = q_enclosed/ε₀.

Move q₁ across the surface: the flux jumps only when the charge crosses it. q₂ stays outside and changes the field on the surface but not the total flux.

Simulation

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Gauss's Law and Electric Flux in 3D

Electrostatics

Gaussian surface Sphere

Surface size R (cm) 3 cm

Charge q₁ (nC) 5 nC

Position of q₁ (cm) 0 cm

Outside charge q₂ (nC) -4 nC

Drag to rotate, two fingers or right-drag to pan, scroll or pinch to zoom. The toolbar has views, cutaway, measure and “show the maths”.

What's happening? Move q₁ across the surface: the flux jumps only when the charge crosses it. q₂ stays outside and changes the field on the surface but not the total flux.

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Where it is in NCERT: Class 12 Physics Part I, “Electric Charges and Fields” (Coulomb's Law, Electric Field, Electric Field Lines, Electric Dipole); Class 12 Physics Part I, “Electrostatic Potential and Capacitance” (Electric Potential, Potential due to an Electric Dipole, Equipotential Surfaces, Potential Energy in an External Field) · ncert.nic.in
Topic notes and formulas: Electrostatics (Electric Charges and Fields, Potential)
Printable formula sheet
Chapter-wise JEE Main PYQs (7)