What changes if the battery stays connected versus disconnected?

With the battery connected the voltage stays fixed, so when C rises by a factor κ the charge Q = CV rises too: the battery pushes extra charge on and the stored energy ½CV² goes up. If the capacitor is charged and then disconnected, Q stays fixed, the voltage drops to 1/κ of its value, and both the field and the energy Q²/2C fall. In both cases the slab is pulled in, and the force is F = ½V²·dC/dx with the voltage at that moment.

Why is a dielectric pulled into a capacitor?

The dielectric becomes polarised, and the non-uniform fringe field at the plate edges pulls on the induced charges toward the inside. It is easiest to compute with energy: the capacitance grows with the inserted length x, so F = ½V²·dC/dx. For parallel plates dC/dx = ε₀w(1/d_eff − 1/d), where w is the plate width and d_eff = d − t + t/κ. When the battery is disconnected, the work done by this force comes out of the energy stored in the capacitor.

What is bound charge and how does it relate to free charge?

In an electric field the molecules of the dielectric stretch into small dipoles. Inside they cancel, but a net charge is left on each surface: the bound or polarisation charge. Its density is σ_b = σ(1 − 1/κ), with the opposite sign to the neighbouring plate, so it weakens the field inside: E_dielectric = E_air/κ. The larger κ is, the closer the bound charge gets to the free charge and the weaker the field inside.

How do I know whether the capacitor will break down?

Every insulator has a dielectric strength, the largest field it can withstand: about 3 MV/m for air and over 100 MV/m for mica. The tool computes the field in the empty part, in the air gap above the slab and in the dielectric, and finds which reaches its own limit first. That gives the breakdown voltage for the current geometry. When the slab does not fill the gap, the field in the remaining air gap is higher than with no slab at all, so the air often fails first.

What is the capacitance of the Earth?

An isolated conducting sphere has C = 4πε₀R. With the Earth's radius of about 6371 km that is roughly 7.1 × 10⁻⁴ F, or about 710 μF, smaller than many ordinary electrolytic capacitors. It shows what a huge unit the farad is. Choose the isolated sphere in the cylindrical/spherical view and press the Earth button to see it.

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🔋Capacitor Simulator - Dielectrics, Parallel Plates, Series & Parallel

This tool covers the main capacitor problems in one place. In the parallel-plate view you drag a dielectric slab partway in and compare a capacitor that stays connected to its battery with one that was charged and then disconnected: capacitance, charge, voltage, field and energy all update, the drawing shows free charge, bound charge and field lines, and you get the force pulling the slab in. Two more views calculate cylindrical, spherical and isolated-sphere capacitors (including the Earth), and the voltage and charge on every capacitor in a series-parallel network.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Capacitor Simulator

1In the parallel-plate view set the plate area, gap and voltage, and pick a dielectric
2Drag the slab on the drawing to change how far it is inserted, and switch between battery connected and disconnected
3Read the capacitance, charge, fields, energy density, pull-in force and breakdown voltage
4Switch to cylindrical/spherical or the network view and enter sizes or capacitor values (4.7u, 100n and so on)

FAQ

What changes if the battery stays connected versus disconnected?: With the battery connected the voltage stays fixed, so when C rises by a factor κ the charge Q = CV rises too: the battery pushes extra charge on and the stored energy ½CV² goes up. If the capacitor is charged and then disconnected, Q stays fixed, the voltage drops to 1/κ of its value, and both the field and the energy Q²/2C fall. In both cases the slab is pulled in, and the force is F = ½V²·dC/dx with the voltage at that moment.
Why is a dielectric pulled into a capacitor?: The dielectric becomes polarised, and the non-uniform fringe field at the plate edges pulls on the induced charges toward the inside. It is easiest to compute with energy: the capacitance grows with the inserted length x, so F = ½V²·dC/dx. For parallel plates dC/dx = ε₀w(1/d_eff − 1/d), where w is the plate width and d_eff = d − t + t/κ. When the battery is disconnected, the work done by this force comes out of the energy stored in the capacitor.
What is bound charge and how does it relate to free charge?: In an electric field the molecules of the dielectric stretch into small dipoles. Inside they cancel, but a net charge is left on each surface: the bound or polarisation charge. Its density is σ_b = σ(1 − 1/κ), with the opposite sign to the neighbouring plate, so it weakens the field inside: E_dielectric = E_air/κ. The larger κ is, the closer the bound charge gets to the free charge and the weaker the field inside.
How do I know whether the capacitor will break down?: Every insulator has a dielectric strength, the largest field it can withstand: about 3 MV/m for air and over 100 MV/m for mica. The tool computes the field in the empty part, in the air gap above the slab and in the dielectric, and finds which reaches its own limit first. That gives the breakdown voltage for the current geometry. When the slab does not fill the gap, the field in the remaining air gap is higher than with no slab at all, so the air often fails first.
What is the capacitance of the Earth?: An isolated conducting sphere has C = 4πε₀R. With the Earth's radius of about 6371 km that is roughly 7.1 × 10⁻⁴ F, or about 710 μF, smaller than many ordinary electrolytic capacitors. It shows what a huge unit the farad is. Choose the isolated sphere in the cylindrical/spherical view and press the Earth button to see it.

Features

Partly inserted slab of any thickness, solved exactly as an air gap in series with the dielectric
Free charges on the plates, bound charges on the dielectric and field lines whose spacing follows E
C, Q, V, E, σ and U together with the pull-in force F = ½V²dC/dx
Presets for air, paper, glass, mica, water, ceramics and more, showing which region breaks down first
Coaxial, concentric-sphere and isolated-sphere capacitors with E(r), including the Earth at about 710 μF
Series-parallel networks: equivalent capacitance plus voltage, charge and energy for every capacitor

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