rvanveshana.com
GAUSSIAN BOUNDARY +44 -44

Live Telemetry & Summary

Observe the boundary crossings:
• Green circles represent inward electric flux (field lines entering the surface).
• Red circles represent outward electric flux (field lines leaving the surface).

💡 Why does Q_out not change Net Flux?

Changing the Outside Charge (Q_out) modifies the field line shape, but every line entering the Gaussian surface (green dot) also exits it (red dot). These cancel out, giving net zero flux from any external charge. Only charges enclosed inside the boundary contribute to the net flux!

Enclosed Charge (Q_enc):44.3 pC
Net Electric Flux (Φ_E):5.00 N·m²/C

Variable Adjuster

Enclosed Charge (Q_enc)44.27pC
-88.5488.54
Outside Charge (Q_out)-44.27pC
-88.5488.54

Gauss's Law

GAUS

Gauss's Law states that the total electric flux through any closed surface is proportional to the enclosed electric charge. Charges outside the surface do not contribute to the net flux because any electric field lines entering the surface must also exit it.

ΦE=∮E⋅dA=Qenclosedε0\Phi_E = \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{enclosed}}{\varepsilon_0}

Whiteboard Solver Steps

Step 1

Gauss's Law Flux Relation

The net electric flux through any closed virtual surface (Gaussian surface) is equal to the net charge enclosed within that surface divided by the permittivity of free space.

ΦE=∮E⋅dA=Qencε0\Phi_E = \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{enc}}{\varepsilon_0}
Step 2

Flux Calculation

Note that charges residing outside the Gaussian surface contribute zero net flux because their field lines enter and exit the closed surface equally.

ΦE=44.27⋅10−128.854⋅10−12=5.00 N⋅m2/C\Phi_E = \frac{44.27 \cdot 10^{-12}}{8.854 \cdot 10^{-12}} = 5.00 \text{ N} \cdot \text{m}^2/\text{C}