Interactive 3D Electrostatics & Parallel Plate Capacitance
C = ε₀ · κ · A / d
🔌 Laboratory Play Area
⚡Connected to DC Battery (+1.50 V). Current flows directly into the capacitor plates!
Connected to Battery
📋 Observation Logger
Trial #
Area A (mm²)
Separation d (mm)
Dielectric κ
Voltage V (V)
Capacitance C (pF)
Plate Charge Q (pC)
Stored Energy U (pJ)
💡 Capacitor Laboratory Help Guide
What is a Capacitor?
A capacitor is an electrical component capable of storing electrical energy in the electrostatic field created between two conducting plates separated by an insulator (dielectric).
In a parallel plate capacitor, connecting a DC potential difference (V) transfers electrons from one plate to the other, creating equal and opposite charges (+Q on the positive plate and −Q on the negative plate).
🌟 Core Learning Goals:
Understand how plate geometry (Area A and separation d) and dielectric constant (κ) govern capacitance (C).
Observe the fundamental relationship Q = C · V and stored potential energy U = ½CV².
Explore the difference between an isolated capacitor (where charge Q remains constant) vs a connected capacitor (where potential difference V remains constant).
Witness discharging through a light bulb converting electrical potential energy into optical and thermal radiation.
Essential Physics Formulas
C =
ε₀ · κ · Ad
where ε₀ = 8.854 × 10⁻¹² F/m (permittivity of free space), κ is the dielectric constant of the medium, A is the plate area (m²), and d is the plate separation distance (m).
Q = C · V ⟺ V =
QC
The electric charge stored on each plate is directly proportional to capacitance and the applied potential difference.
U = ½CV² =
Q²2C
= ½QV
Electrostatic potential energy stored in the electric field between the plates.
E =
Vd
=
σε₀ · κ
Uniform electric field strength between the parallel plates, where σ = Q / A is the surface charge density.
Interactive Laboratory Controls
2D Interactive Playground: Direct hands-on laboratory workbench! Drag the Top Plate to change separation d (2.0–10.0 mm); drag the Right Edge handle to resize plate Area A (100–400 mm²); drag the Dielectric Slab horizontally in and out of the plates; flip the 3-Way Knife Switch to connect Battery, Isolate, or discharge through the Light Bulb; and drag the Voltmeter Probes anywhere on the circuit!
Plate Area (A): Precision numerical input (100.0 mm² to 400.0 mm²). Plates smoothly expand or contract in 3D.
Plate Separation (d): Adjust distance from 2.0 mm to 10.0 mm. Plates physically move along the vertical axis in real-time.
Battery Voltage (V): Control DC potential from −1.50 V to +1.50 V. Positive voltage charges top plate positively; negative voltage flips polarity smoothly.
Dielectric Selector (κ): Choose Air (1.0), Teflon (2.1), Paper (3.5), Glass (5.0), or Custom. Watch the translucent 3D slab glide between the plates!
3-Way Knife Switch:
Battery: Capacitor charges and maintains source potential difference.
Isolated: Capacitor is disconnected from the battery. Trapped charge Q remains strictly constant!
Light Bulb: Discharges stored charge through the filament, producing a brilliant golden-orange 3D flash that exponentially decays.
Key Physics Experiments
Verify Capacitance vs Area: Fix separation at d = 5.0 mm and voltage at 1.50 V. Double plate area from 100 mm² to 200 mm². Observe capacitance and stored charge double!
Verify Capacitance vs Separation: Halve the distance d from 10.0 mm to 5.0 mm. Notice capacitance and field intensity both double.
Isolated Plate Separation (Mechanical Work): Charge to 1.50 V, flip the knife switch to Isolated, then increase plate separation d. Charge Q stays locked, while voltage V and energy U increase proportionally because mechanical work was performed against the electrostatic attraction!
Dielectric Polarization: Switch to Isolated mode and insert Glass (κ = 5.0). Observe voltage drop by factor of 5 as bound charges neutralize field!
Bulb Discharge Energy Dissipation: Charge the capacitor fully, flip switch to Light Bulb, and observe optical emission decaying as stored energy dissipates.
Frequently Asked Questions
Q: Why does capacitance increase when a dielectric is inserted?
A: Molecules in the dielectric polarize under the electric field, creating opposing surface charges that weaken the internal field. When connected to a battery, extra charge flows in from the source to restore potential difference, raising capacitance by factor κ.
Q: Why does voltage increase when plates are separated in isolated mode?
A: In isolated mode, electric charge cannot escape (Q is constant). As separation d increases, capacitance decreases (C ∝ 1/d). Hence V = Q / C must increase! The external mechanical work performed against electrostatic attraction is converted into stored electrostatic energy (U = Q² / 2C).
Q: What causes the light bulb glow to decay exponentially?
A: The discharge current is governed by Ohm's Law and charge drainage: I(t) = (V₀ / R) · e−t / RC. Bulb illumination brightness is proportional to I², producing a rapid flash followed by a smooth exponential fade.
