## Concept explanation An **electric charge** acts like a source or sink for the **electric field** in space. A positive charge sends field lines outward, while a negative charge pulls them inward. The field is strongest close to the charge and weakens with distance, which is why the density map fades away from the center. **Gauss’s law** connects this picture to electric flux: the total outward flux through any closed loop depends on the amount of enclosed charge, and its sign tells you whether the field is flowing out of the loop or into it. ## What you see You’re looking at a 2D slice of space around one point charge. The central disk is the charge, the arrows show the local field direction, and the faint colored density map shows where the field magnitude is large or small. The circular Gaussian loop is a sample closed boundary for thinking about flux, and the flux readout changes continuously as the charge slider moves from negative through zero to positive. ## Try it yourself - **Drag the charge slider** from positive to negative and watch the arrows reverse direction as the field changes from a source to a sink. - **Pause near `q = 0`** and notice how the arrows shrink and the density map fades, showing that the field magnitude and flux both approach zero. - **Move the slider slowly across zero** to see the field regrow with the opposite direction, linking the sign of charge to the sign of electric flux. - **Switch between arrow densities** to compare a simpler directional picture with a more detailed field pattern. - **Toggle the Gaussian loop** and compare the `flux ∝ q` readout with the direction of the arrows crossing the loop. - **Press Reset** to return to a clearly positive charge and replay the sign change again. ## Concept explanation **Electric flux** measures how much electric field passes through a **closed surface**. Gauss’s law says the total flux depends only on the **net enclosed charge** inside that boundary. Charges outside the boundary can bend and reshape the field lines nearby, but their contributions cancel overall, so they do not change the total flux through the closed loop. ## What you see You’re looking at several draggable point charges and one circular closed boundary. Small arrows across the canvas show the local electric field direction, while the short colored arrows on the circle mark where field crosses the boundary: teal means outward and red means inward. The flux badge updates with the current value of `Φ`, which here tracks the net enclosed charge. ## Try it yourself - **Drag a positive charge into the circle** and watch the flux value increase. - **Drag a negative charge into the circle** and notice the flux value decrease. - **Move charges around outside the circle** and see that the field pattern changes while the total flux stays the same. - **Use the boundary radius slider** to include or exclude charges and compare the new flux. - **Switch the charge layout** to the outside-pair setup, then **move only outside charges around** to test that outside motion alone does not change total flux. - **Turn field arrows on or off** to focus either on the overall pattern or on the boundary crossing arrows. ## Concept explanation When an electric **current** flows through a wire, it creates a **magnetic field** that circles the wire in closed loops. The field does not spread straight outward from the wire the way light rays might; instead, every field line wraps around the current. This matches **Ampère’s law** intuition: current acts like a source of circulation, so the magnetic field has a curling pattern. If the current reverses direction, the magnetic loops reverse too, but they still remain closed loops rather than beginning or ending anywhere. ## What you see You are looking at the end of a straight wire at the center of the screen. The symbol in the middle shows whether the current points out of the screen or into it, while the surrounding rings represent magnetic field lines. Small arrows on those rings show which way the field circulates, and the pattern becomes tighter and stronger as the current magnitude increases. Near zero current, the loops fade because the magnetic effect is weak. ## Try it yourself - **Drag the current slider toward positive values** and watch the loops tighten and the field grow stronger around the wire. - **Move the slider through `0` to negative values** and notice that every arrow flips direction while the field still forms closed circles. - **Pause near `0`** and observe how the field nearly disappears instead of pointing radially away from the wire. - **Toggle the loop arrows on and off** to focus either on the circular geometry of the field lines or on their circulation direction. - **Press `Reset`** and then compare a large positive current with an equally large negative current to see that the strength can match even when the loop direction reverses. ## Concept explanation A **magnetic field** is different from an electric field made by isolated charges because magnets do not come with standalone **magnetic monopoles**. That means magnetic field lines never start on a lone north pole or stop on a lone south pole. Instead, every field line forms a **continuous loop**: outside a bar magnet the field goes from north to south, and inside the magnet it continues from south back to north. This is the idea behind **Gauss’s law for magnetism**, which says the net magnetic flux through any closed surface is zero. ## What you see You’re looking at a bar magnet with teal field loops drawn around it. The arrows show the direction of the field outside the magnet and, when the interior paths are shown, back through the magnet so the loops close. When you split the magnet, each half becomes its own smaller dipole with a north and south pole, so the field redraws into new closed loops around each piece instead of leaving broken line ends in the gap. ## Try it yourself - **Click the Split magnet button** and watch the single dipole turn into two smaller magnets. - **Click Reunite magnet** to bring the halves back together and compare the loop pattern. - **Move the field line count slider** to make the looping structure more sparse or more dense. - **Toggle Show through-magnet paths** to reveal or hide the part of each loop that continues through the magnet. - **Notice the gap when the magnet is split**: you still do not see field lines ending in empty space, because each piece keeps a complete north–south loop pattern. ## Concept explanation A **changing magnetic field** creates a **circulating electric field** around it. This is the core idea of **Faraday’s law**: induction depends on how fast the magnetic field is changing, not just on whether a magnetic field is present. If the magnetic field grows or shrinks quickly, the induced electric field is stronger. If the magnetic field momentarily stops changing, the induced electric field fades even when the magnetic field itself is still large. ## What you see Inside the central circle, the symbol density shows the magnetic field passing through the screen: denser symbols mean a larger magnetic field magnitude, and the symbol type switches when the field reverses direction. Around that region, teal arrows form circular rings representing the induced electric field. Their length and number increase when the magnetic field changes faster, and their direction flips when the magnetic change reverses sign. ## Try it yourself - **Drag the magnetic change rate slider** to the right and watch the electric arrows strengthen when the field is increasing. - **Drag the slider left through zero** and notice the circular electric field reverse direction as the magnetic change reverses. - **Set the slider near `0`** and observe that the electric arrows nearly disappear, even though magnetic symbols can still remain inside the circle. - **Press `Pause`** to freeze one moment and compare the readouts for `B` and `dB/dt`. - **Press `Reset`** and then **sweep the slider slowly from negative to positive** to connect arrow direction directly to the sign of `dB/dt`. ## Concept explanation A **changing electric field** can create a **magnetic field** even where no charge is physically crossing the space. In a charging capacitor, conduction current flows in the wires, but between the plates there is only changing electric flux. Maxwell’s key insight was to treat that changing flux like a **displacement current**, so Ampère’s law gives the same magnetic circulation whether you imagine a surface cutting through the wire or a surface stretched across the empty gap. ## What you see You’re looking at two capacitor plates with electric field arrows drawn between them. The time control changes the capacitor’s charge, so the field in the gap grows, shrinks, and reverses. Circular magnetic loops surround both the wire path and the plate gap; when the electric field changes quickly, those loops become stronger and larger, including in the empty region between the plates where no charges directly pass. ## Try it yourself - **Drag the time slider** to moments when the electric arrows are longest, then notice that the magnetic loops are small because the field is large but not changing much at that instant. - **Move the time slider through the midpoint** of the cycle and watch the magnetic loops grow, showing that the strongest magnetic effect comes from the largest `dE/dt`. - **Switch the drive mode** between `Sine` and `Triangle` to compare smooth versus nearly constant-rate charging, and see how the loop strength follows the rate of change rather than the field itself. - **Adjust the plate gap** and compare the same circular magnetic pattern around the wire and around the empty space between the plates. - **Press Reset** and then trace the two labeled surfaces mentally: one can cut the wire, while the other spans the gap, yet both must predict the same magnetic circulation. ## Concept explanation An **electromagnetic wave** is a self-propagating pattern of changing fields: a changing **electric field** creates a magnetic field, and a changing **magnetic field** creates an electric field. That mutual regeneration lets the disturbance move through space without needing a material medium. In the wave shown here, the electric field oscillates vertically, the magnetic field oscillates horizontally, and the wave travels to the right, with all three directions staying at right angles to one another. ## What you see You’re looking at a perspective view of one wave moving rightward. The blue curve represents the electric field, the teal curve represents the magnetic field, and the gold arrows show the forward direction of energy flow. The axis guides and the highlighted field vectors help you see that no matter how you orbit the camera, the electric field, magnetic field, and travel direction remain perpendicular. ## Try it yourself - **Drag anywhere in the main view** to orbit the scene and check that the blue electric field, teal magnetic field, and rightward travel direction stay at `90°` to each other from every angle. - **Increase the frequency slider** and watch the crests pack closer together, showing a shorter wavelength. - **Decrease the frequency slider** to spread the crests farther apart and make the wavelength longer. - **Increase the amplitude slider** to make both field oscillations larger at the same time. - **Compare the gold energy arrows with the two field directions** and notice that energy keeps flowing forward even while each field oscillates sideways. - **Pause on one highlighted E and B vector pair** and mentally trace how each changing field supports the other as the whole pattern advances to the right. ## Concept explanation **Maxwell’s equations** are a unified set because they all relate fields to either **sources**, **circulation around a loop**, or **change over time**. Electric fields can begin or end on electric charge, magnetic fields instead form closed loops around currents, and changing magnetic or electric fields can create circulating fields even when no ordinary source sits at the center. Together, the four equations show one repeating pattern: what is enclosed by a surface or loop determines how the field behaves there. ## What you see You’re looking at a four-panel comparison. The top-left panel shows electric flux spreading from charge, the top-right shows magnetic loops around current, the bottom-left shows electric circulation induced by changing magnetic flux, and the bottom-right shows magnetic circulation induced by changing electric flux in a capacitor. Small labels highlight the structural idea in each panel: whether the field **starts on charge**, **forms closed loops**, or **appears due to change**. ## Try it yourself - **Click each preset button** to spotlight one equation while keeping the other three visible for comparison. - In the electric-flux view, **move the enclosed charge slider** and notice how the radial field grows, reverses, or disappears as the source changes sign or goes to `0`. - In the magnetic-loops view, **adjust the current slider** and watch the field circulate around the wire instead of starting or ending on it. - In the induced-electric view, **change the magnetic change rate** to see circulating electric field loops appear only when the magnetic flux is changing. - In the induced-magnetic view, **change the capacitor charging rate** and compare it to the magnetic-loops panel: both create magnetic circulation, but one comes from conduction current and the other from changing electric field. - **Compare the panels side by side** and ask yourself which equations are about enclosed source, which are about closed loops, and which only activate when something changes in time.