The previous parts treated voltage as something a battery provides and a resistor drops. That description works for calculations but glosses over what voltage actually is: a difference in the potential energy of charge between two points, maintained by a physical thing, a field, that exists in the space around and between components.
What a field is
A field is an influence that fills space and acts on anything susceptible to it. Gravity is the familiar one: the Earth creates a gravitational field, and anything with mass placed anywhere in that field feels a force; no contact needed, no wire connecting them. The field is the mechanism.
An electric field works the same way, for charge instead of mass. Any charged object creates an electric field in the space around it. Place another charge in that field and it feels a force: opposite charges attract, same charges repel. The field is real, it occupies space, and it does work.
The electric field
A single positive charge sends field lines radiating outward in all directions, weakening with distance. A negative charge draws them inward. Two opposite charges sitting together largely cancel their fields at any distance: the two sets of lines point in opposite directions and subtract. The result is almost no net field in the space around them.
Separate those charges and the cancellation is lost. In the region between them, both fields point the same way and add. More field now occupies space than when the charges were together, and creating that extra field required work. That work is stored in the field itself, as energy distributed across the volume it occupies. This is not a metaphor: the energy is physically there, and it does work when the field collapses.
This is why opposite charges attract: the together state has less field, less energy. Releasing them lets the system fall to the lower-energy configuration, the same way a ball rolls downhill.
A capacitor exploits this directly. Two large plates, close together, one positive and one negative, trap a strong uniform field in the gap between them.
The energy lives in that field, not in the plates themselves, but in the space between them. Disconnect the battery and the field persists, held in place by the charge imbalance, ready to do work when the charges are given a path to recombine.Voltage is a potential difference
Electric potential at a point is the potential energy per coulomb at that location. Voltage (what a voltmeter reads) is the difference in potential between two points. A strong electric field means potential changes steeply with distance; a weak field means it changes gently. The field is the slope; the potential is the height.
Between the capacitor plates, potential is higher at the positive plate and lower at the negative. The voltage across the capacitor is that difference, and the field between the plates is what maintains it.
Ground is the reference, defined as zero potential. It is not special because it has zero charge; it is special because the Earth is large enough that any charge transferred to or from it shifts its potential by an unmeasurable amount. It is a stable anchor, the same way sea level is used as the reference for height: not the lowest point possible, just a convenient fixed reference.
The magnetic field
A moving charge (a current) creates a second kind of field: a magnetic field. Where the electric field points radially from charges, the magnetic field forms rings around the current, circling the wire in closed loops. Direction follows the right-hand rule: thumb along conventional current, fingers curl in the direction of the field.
A straight wire gives a weak, diffuse field. Bend the wire into a loop and the field lines through the centre all reinforce. Wind many loops into a coil and you get a strong, uniform field running straight through the inside, exactly like a bar magnet but switchable by controlling the current. That is an inductor.
Building the current takes work. As the magnetic field grows, it pushes back against the change, inducing a voltage that opposes the increasing current. That work is stored in the field. Cut the current and the field collapses, releasing its stored energy as a brief voltage spike that tries to maintain the current. This is the inductor's defining behaviour, covered in the next part.
Two components, one principle
Resistors convert energy to heat immediately. Capacitors and inductors store it in fields and give it back. That single difference, storage versus dissipation, determines how they behave in a circuit.
| Component | Field | Resists change in |
|---|---|---|
| Capacitor | Electric, between plates | voltage |
| Inductor | Magnetic, inside coil | current |
The filling and emptying of a field takes time, and time is how these components shape signals, filter frequencies, and give circuits memory. The next part covers how they behave when connected and switched.
The electric and magnetic fields described here are two aspects of one thing: the electromagnetic field. How they generate each other, and how that relationship produces light, is the subject of the part after that.
Where this comes from
- Electric and magnetic fields, potential, energy density: Griffiths, Introduction to Electrodynamics, ch. 2 to 7.
- Accessible treatment: Purcell and Morin, Electricity and Magnetism, ch. 1 to 7.
Check yourself
1. Two positive charges are pushed toward each other. Does the total electric field energy in space increase or decrease?
Increases. Same-sign charges have fields pointing in the same direction between them; they add rather than cancel. Pushing the charges closer enlarges that region of reinforced field, requiring work, which is stored as increased field energy.
2. A capacitor is charged and disconnected from the battery. Where is the energy stored?
In the electric field between the plates, not in either plate alone. The charge imbalance on the plates maintains the field, and the field holds the energy.
3. A wire carries 2 A. You cut the current to zero. What happens to the magnetic field around the wire?
It collapses to zero. No moving charge means no magnetic field. As it collapses, the changing field induces a brief voltage spike in the wire, trying to maintain the current.
4. Why is ground defined as zero volts, and does that mean the Earth carries no charge?
Ground is zero by convention: a chosen reference, not a physical property. The Earth is not necessarily charge-neutral; it is used as reference because it is large enough that any practical charge transfer does not shift its potential measurably.