The charges and the observer can all be moved.
The charge can be changed by selecting it and then adjusting the slider.

You can drag more charges and observers out from the two square boxes at the top right hand corner. Drag them back to remove.
To add equipotential, first select an observer then click the "Add equipotential" button.
Tip: Try not to show both field lines and equipotentials at the same time otherwise it may look too messy. You can control this by using the show/hide buttons.
Can you see the electric field always points perpendicular to the equipotentials?

Electric Flux

Electric flux is the amount of electric field captured by a surface. Adjust the sliders to see how the total flux changes.

Gauss' Law

• Electric flux $\Phi$ measures the amount of E field captured by a surface.
• Outward E field gives positive contribution to the flux.
• Inward E field gives negative contribution to the flux.
• A curved surface can be divided into small areas, each contributing to the flux. The area vectors ($d\vec A$, i.e. normal vector) are defined to point outward.
• Summing up the flux for each small area gives the total flux $\Phi = \oint \vec E \cdot d\vec A$.
• Gauss' law states $\Phi = \frac{q_{enclosed}}{\epsilon_0}$.

Charge Enclosed by a Gaussian Surface

• Drag or adjust the radius of the Gaussian surface and observe how the charge enclosed changes.

Gauss' Law with Adjustable Gaussian Surface in 2D

• Total charge on all three charge configurations is $100nC$.
• Adjust the radius of the Gaussian surface and observe how the charge enclosed changes.
• Use the equation below to verify the amount of charge at different radius for different charge configurations.

Electric Potential of Two Charges

The charges and the observer can all be moved.
The charge can be changed by selecting it and then adjusting the slider.

Relation between Electric Potential and Electric Field

• Electric field represents the rate of change of potential. It points from high $V$ to low $V$.
• E.g.: $E_x=2V/m$ means if you move $1m$ to the right, your potential will decrease by $2V$.
• Graphically, $E_x = -1 \times $ (the slope of the $V$ vs $x$ graph). The steeper the curve, the stronger is the field.
• Analogy with mechanics:
• Potentials $V$ in electricity is like height $h$ in mechanics. An object rolls from high $h$ to low $h$. A positive charge moves from high $V$ to low $V$.
• Negative charge moves opposite to positive charge. You could imagine if negative mass exists, they will fly into the air instead of falling.

Electric Potential Energy

The charges and the observer can all be moved.
The charge can be changed by selecting it and then adjusting the slider.

Electric Field of a Line of Charge

A Sheet of Charge

Make Your Own Electric Field