To investigate the electrostatic potential distribution in a two-dimensional conducting medium for uniform parallel-plate and non-uniform dipole electrode configurations, map equipotential contours, verify the strict spatial orthogonality between electric field lines and equipotential surfaces, measure the electric potential gradient (E = −dV/dx), and determine the uniform electric field strength using ordinary least-squares linear regression. Explore a virtual apparatus, collect readings and analyse a graph.
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Timing is generated from the model; a short on-screen trial represents a longer physical interval. Animation is illustrative.
The theoretical model assumes perfectly planar parallel electrodes of infinite length with zero contact resistance, perfectly uniform and isotropic graphite conductivity across the Teledeltos paper, and an ideal infinite-impedance voltmeter. In a physical laboratory, finite electrode length introduces edge fringing fields (causing outward bowing of equipotentials beyond ±6 cm from the central axis), paper manufacturing anisotropic grain introduces minor directional resistivity variations (~1 to 2%), and localized contact resistance at the probe tip introduces small experimental reading scatter.
Precision insulated mounting board supporting a 30 cm × 40 cm sheet of uniform carbon-graphite conducting paper, underlaid with a transparent 1 mm metric Cartesian coordinate grid for high-precision probe tracking.
Pair of matched, heavy machined brass bar electrodes (length L = 20.0 cm, width 1.0 cm, thickness 0.5 cm) clamped securely onto the conducting paper with colloidal silver conductive paint to establish uniform parallel equipotential boundaries.
Low-noise laboratory DC power supply (0 to 15.00 V, 1.0 A current limit) providing an ultra-stable 10.00 V potential difference across the boundary electrodes.
Digital multimeter with 10.0 MΩ input resistance and 1 mV voltage resolution, designed to sample local surface potentials without drawing significant loading current from the carbon sheet.
Insulated handheld copper-beryllium stylus probe with fine point contact for pinpointing exact Cartesian coordinates and sensing local surface potential without puncturing or tearing the conducting substrate.
Set of brass point electrodes and concentric rings (inner cylinder r₁ = 1.0 cm, outer ring r₂ = 8.0 cm) for investigating non-uniform, radial logarithmic, and dipole field topologies.
To investigate the electrostatic potential distribution in a two-dimensional conducting medium for uniform parallel-plate and non-uniform dipole electrode configurations, map equipotential contours, verify the strict spatial orthogonality between electric field lines and equipotential surfaces, measure the electric potential gradient (E = −dV/dx), and determine the uniform electric field strength using ordinary least-squares linear regression. Suggested independent settings: 1.5, 3.0, 4.5, 6.0, 7.5, 9.0 cm.
Fasten a fresh sheet of Teledeltos conducting paper smoothly onto the mapping board. Place the two parallel brass bar electrodes exactly d = 10.00 cm apart along the calibrated grid lines. Apply a thin line of colloidal silver conductive paint beneath each electrode to ensure flawless, uniform ohmic contact with the graphite substrate, and clamp firmly.
Colloidal silver eliminates contact resistance variations along the electrode edges, ensuring the brass bars act as strictly equipotential boundary surfaces.
Connect the positive terminal of the regulated DC power supply to the right electrode (+10.00 V) and the negative terminal to the left electrode (0.00 V / Ground). Connect the common (COM) ground lead of the digital voltmeter directly to the left grounded electrode, and connect the positive voltmeter lead to the handheld tracking probe.
Grounding the negative electrode establishes an unambiguous zero-potential reference datum for all subsequent probe measurements across the board.
Set the voltmeter to DC millivolts/volts. Gently touch the tracking probe to the conducting paper and locate points having potentials of exactly 2.00 V, 4.00 V, 6.00 V, and 8.00 V. For each voltage level, locate at least 7 distinct (x, y) coordinates spanning across the board, and record their positions on the coordinate grid sheet.
Finding multiple points of equal potential maps the full two-dimensional contour lines of the electrostatic field.
Connect the points of equal potential with smooth continuous curves to produce equipotential lines. Using a drafting square, construct a family of electric field lines that start at the +10 V electrode and terminate on the 0 V electrode, ensuring every field line intersects every equipotential line at an angle of strictly 90°.
Because electrostatic force is conservative, the gradient vector E = −∇V is perpendicular to surfaces of constant potential at every spatial point.
Position the tracking probe along the central longitudinal axis of symmetry (y = 0) where edge fringing fields are negligible. Record the local potential V for six discrete displacements x from the grounded electrode (x = 1.5, 3.0, 4.5, 6.0, 7.5, and 9.0 cm). Verify that the voltmeter reading stabilizes before logging data.
Sampling along the central axis isolates the uniform one-dimensional potential gradient dV/dx, minimizing two-dimensional edge distortions.
Replace the parallel plates with two cylindrical point electrodes (+q and −q separated by 10 cm). Trace the resulting curved equipotential ovals and observe the convergence of electric field lines near the point poles, verifying that electric field density is greatest where equipotentials are closest together.
Comparing planar and dipole geometries reinforces the universal relationship between field intensity, surface curvature, and equipotential line spacing.
Points are your observations. The fit uses SI x and y values before display scaling.
| # | Probe displacement x (cm) | Measured electric potential V (V) | Probe displacement x (m) | Electric potential V (V) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.