## Concept explanation An **electric field** shows the direction a positive test charge would be pushed and gives a sense of the field’s **relative strength** at different places in space. Around a single point charge, the field is strongest close to the charge and weaker farther away, so the arrows near the center are longer and more concentrated. A **positive charge** creates a field pointing outward, while a **negative charge** creates a field pointing inward. ## What you see You are looking at one central particle with field arrows arranged radially around it. The arrow pattern stays strongest near the center and weaker toward the edges, while the button lets you reverse only the direction of the arrows by switching the charge from `+` to `−`. The optional rings help you compare distance from the charge without changing the underlying field pattern. ## Try it yourself - **Click the `Switch sign` button** and watch every arrow reverse direction at once while the overall strength pattern stays the same. - **Look near the center** and notice that the arrows are longer there, showing a stronger field close to the charge. - **Compare the outer arrows to the inner arrows** to see how the field becomes weaker farther away. - **Move the `Field density` slider** to add or remove arrows and make the radial pattern easier to inspect. - **Toggle `Show strength rings`** to help judge how field strength changes with distance from the particle. - **Click inside the main canvas** for a quick sign flip and confirm again that only direction depends on whether the charge is positive or negative. ## Concept explanation An **electric field** tells you which way a positive test charge would be pushed and how strongly it would be pushed at each point in space. With **superposition**, fields from different charges do not replace one another — they **add vectorially**. That means each charge contributes its own field at a location, and the **net field** is the direction-and-strength result of combining those contributions tip-to-tail. ## What you see You are looking at two movable charges on a dark 2D plane, with a grid of arrows showing the combined field everywhere. The small teal arrows represent the total field across the region, while the highlighted test point shows the local result more clearly with a larger white net-field arrow. When contribution arrows are enabled, you can also compare the separate influence of each charge at that point and see how their overlap creates the final answer. ## Try it yourself - **Drag either charge** to a new location and watch the whole arrow pattern update instantly. - **Move the test point** and compare how the local net field changes in different regions. - **Turn on the contribution view** to see the two individual field vectors that add to the larger net vector. - **Slide the test point x-position control** to sweep the highlighted point across the plane and notice where the net field gets stronger or weaker. - **Increase the arrow scale** to make differences in field strength easier to see. - **Change the grid density** to compare the broad field pattern with a more detailed local view. - **Reset positions** and then place the charges closer together or farther apart to see how superposition reshapes the field everywhere. ## Concept explanation When an **electric current** flows through a straight wire, it creates a **magnetic field** in the space around it. That field does not point straight outward or along the wire — it wraps around the wire in **concentric circles**. The **strength** of the field depends on the current’s magnitude, so a larger current makes the field stronger, and the **direction** of the field depends on the current’s sign. You can predict the direction with the **right-hand rule**: point your thumb in the direction of the current, and your curled fingers show the direction of the magnetic field. ## What you see You are looking at a vertical wire in the middle of the view with circular magnetic field lines looping around it. Small arrows placed on the circles show which way the magnetic field points as it circles the wire. The slider changes the current from negative to positive values, so the circles become more pronounced as the magnitude grows, while the arrows reverse when the current changes direction. The hand guide on the left gives a visual cue for the right-hand rule. ## Try it yourself - **Move the current slider toward `0`** and notice how the field lines fade, showing that little or no current produces little or no magnetic field. - **Increase the current to a large positive value** and watch the circles become stronger and more numerous while the arrows circle in one direction. - **Drag the slider into negative values** and look for the arrows to reverse, showing that flipping current direction flips magnetic field direction. - **Compare `+8` and `-8`** to see that the field strength is similar for equal magnitude, even though the direction is opposite. - **Use the hand guide on the left** or **drag the hand marker** to connect thumb direction along the wire with the curl direction of the field. - **Press `Auto cycle`** to sweep through positive and negative current values and see the reversal happen continuously. ## Concept explanation A **moving charge** in a **magnetic field** feels a force that points at right angles to both the charge’s velocity and the field direction. That means the magnetic force does not push the particle forward or backward along its motion; instead, it continually nudges the particle sideways, which bends the path into a curve. The force depends on the direction of motion, and if you reverse the sign of the charge from positive to negative, the force direction flips as well. ## What you see The repeated circled `+` symbols show a uniform magnetic field pointing out of the screen. The particle carries either a positive or negative charge, with a teal arrow for velocity `v` and a gold arrow for magnetic force `F`. As the particle moves, its trail shows the curved path caused by the sideways magnetic force, while the control panel lets you change speed, field strength, and charge sign. ## Try it yourself - **Drag the velocity arrow** to point in a new direction and watch the force arrow instantly swing to stay perpendicular. - **Click the charge button** to switch from positive to negative charge and see the force reverse. - **Increase the speed slider** and notice how a faster particle bends more strongly and traces a tighter-changing path. - **Adjust the field strength slider** to compare weak and strong magnetic fields. - **Press `Reset path`** after changing settings so you can clearly see the new curve from the start. - **Try aiming the velocity left, right, up, and down** and compare how the force direction changes each time. ## Concept explanation A **changing electric field** does not stay isolated: as it grows or reverses, it produces a **magnetic field** that wraps around it. The reverse is also true — a **changing magnetic field** produces an electric field. This mutual generation is the core of **electromagnetic waves**. Instead of thinking of electric and magnetic fields as separate effects, you can think of them as a linked pair that continually drives one another whenever either one changes over time. ## What you see In the center, the blue vertical arrows represent the electric field, growing and shrinking as the oscillation changes. Around that region, the gold dashed loops represent the magnetic field circling the same area. Their size and direction update together, so when the electric field changes faster, the magnetic loops also change faster. The labels help you distinguish the two field types while the live readout shows the shared oscillation rate and current field strength. ## Try it yourself - **Move the oscillation speed slider** and watch both the blue electric arrows and gold magnetic loops speed up or slow down together. - **Press Pause** to freeze the pattern and inspect one moment of the linked fields, then **press Play** to resume the oscillation. - **Set a low speed** and notice how the changing electric field and magnetic field are easier to follow as one coordinated cycle. - **Set a high speed** and observe that neither field changes independently; both respond to the same time-varying oscillation. - **Watch for the reversal** when the electric arrows flip direction, and notice that the magnetic loop circulation flips with them. ## Concept explanation An **electromagnetic wave** is made of two linked oscillations: an **electric field** and a **magnetic field**. As the wave travels forward through space, the electric field vibrates in one direction while the magnetic field vibrates in a direction at right angles to it. Both are also perpendicular to the direction the wave moves, so together they form a three-way geometric relationship: electric field, magnetic field, and propagation direction are all mutually perpendicular. ## What you see You are looking at a 3D wave moving horizontally along the `x` direction. The blue curve shows the electric field rising and falling vertically, while the teal curve shows the magnetic field oscillating sideways in a perpendicular direction. The connecting line segments help you see that both fields are attached to the same traveling wave pattern, and the gold arrow marks the direction in which the wave propagates. ## Try it yourself - **Drag the scene** to orbit the camera and check that the blue and teal oscillations stay at right angles from every viewing angle. - **Move the wavelength slider** to change the spacing between crests and troughs, and notice how both fields stretch or compress together. - **Move the amplitude slider** to make both oscillations taller, and see that the electric and magnetic fields still remain perpendicular. - **Compare the two curves** and notice that their peaks and zero-crossings line up as the wave travels. - **Look along the gold arrow direction** and confirm the geometric rule: one field points up-down, one points sideways, and the wave moves forward.