Charge, attraction and repulsion

Electric charge is a conserved property of matter that makes an object experience electric forces in an electric field. Charge comes in two signs: positive and negative. Like charges repel; unlike charges attract. A neutral object has equal total positive charge and total negative charge, so its net charge is zero.

In everyday electrostatics, electrons are almost always the charges that move. A negatively charged object has extra electrons. A positively charged object is short of electrons. Use that wording in explanations: protons normally stay fixed inside nuclei in solids, while electrons act as the mobile charge carriers.

A charged object can attract a neutral conductor or insulator by causing polarization, a separation of charge within an object while the object remains neutral overall. The nearer separated charge has the opposite sign, so its attraction is stronger than the repulsion from the farther separated charge.

Coulomb’s law

Coulomb’s law is an inverse-square law for the electrostatic force between two point charges. For charged bodies treated as point charges,

F = k q₁q₂ / r², where F is the electrostatic force between the charges (N), k is Coulomb’s constant (N m² C⁻²), q₁ is the charge of the first point charge (C), q₂ is the charge of the second point charge (C), and r is the separation between the point charges (m).

The sign of q₁q₂ tells you what kind of force it is: a positive product gives repulsion, and a negative product gives attraction. The force acts along the straight line joining the point charges. If direction matters, don’t leave a Coulomb’s-law answer as just a number.

Coulomb’s constant can be written as

k = 1/(4πε₀), where ε₀ is the permittivity of free space (C² N⁻¹ m⁻²). In a material medium we use

k = 1/(4πε), where ε is the permittivity of the medium (C² N⁻¹ m⁻²). A larger permittivity gives a smaller force for the same charges and separation. Air is extremely close to a vacuum for most school calculations, but materials such as water, paper or rubber have different permittivities, so Coulomb-force calculations may give different results in different media.

How permittivity changes Coulomb force for the same charges and separation.

Coulomb’s original torsion-balance work gave an experimental route to the inverse-square relationship. A modern school version can use two small conducting-coated spheres on insulating supports: vary the separation and use a balance reading or sideways displacement as a force indicator. The atmosphere must be dry, the charges leak away easily, and high-voltage supplies need sensible handling. If the force indicator is proportional to F, a plot against 1/r² should be linear.

Conservation and transfer of charge

Conservation of electric charge is the principle that the total electric charge of an isolated system remains constant. Charge can move from one object to another, or around a circuit junction, but the process does not create or destroy charge. At a junction, this is why total current into the junction equals total current out.

Charge can be transferred in three syllabus ways.

• Charging by friction is charge transfer caused by rubbing two materials together so that electrons move from one surface to the other. The two objects finish with opposite signs of charge.
• Charging by contact is charge transfer caused by touching a charged object to another object. The initially uncharged object finishes with the same sign of charge as the charged object, although the original object’s charge is reduced.
• Electrostatic induction is charging a conductor without contact by using a nearby charged object to separate charges, then using grounding to allow one sign of charge to leave or enter.

Grounding or earthing means connecting an object to Earth with a conductor so charge can flow between the object and Earth until they are at the same potential. For example, bring a negatively charged rod near a neutral conducting sphere and electrons in the sphere are repelled. If the sphere is grounded while the rod remains nearby, electrons can flow to Earth. Removing the ground connection before removing the rod leaves the sphere positively charged. If the inducing rod were positive, electrons would be drawn from Earth and the sphere would finish negative.

Millikan’s experiment and quantized charge

Quantization is a property of a physical quantity that can take only discrete values rather than a continuous range. Millikan’s oil-drop experiment provides evidence that electric charge is quantized.

In Millikan’s method, tiny oil drops are charged and observed between two horizontal plates. First, the motion of a falling drop with no electric field is used to determine its weight, allowing for drag and buoyancy. Then a uniform electric field is adjusted so that the same drop is stationary. At rest, the electric force balances the effective weight of the drop. Repeating this for many droplets shows that measured charges are always integer multiples of one smallest charge: the elementary charge.

The elementary charge is the magnitude of the charge of a proton or electron. Its exact value is e = 1.602176634 × 10⁻¹⁹ C, where e is the elementary charge (C). A proton has charge +e and an electron has charge −e.

This experiment also works well as a nature-of-science example. Millikan’s result was close to the modern value, but later examination of the data selection raised questions about rejected measurements and experimental bias. The physics conclusion remains: no smaller free charge than e appears in ordinary matter. Other quantities you meet later are also quantized, for example atomic energy levels and angular momentum in simple atomic models.

Electric field strength

Electric field strength is a vector quantity equal to the force per unit positive test charge placed at a point. It is defined by

E = F / q, where E is electric field strength (N C⁻¹), and q is the charge of the positive test charge (C).

The direction of E is the direction of the force on a positive test charge. Put a negative charge in the same field and it experiences a force in the opposite direction. The “test charge” is a thought experiment: in reality, any charge you place in a field also has its own field and can disturb the arrangement you are trying to measure.

For a point source charge,

E = kQ / r², where Q is the source charge producing the field (C). The field points away from a positive source charge and towards a negative source charge. With more than one source charge, electric field strengths add as vectors. Along a line, take care with signs; off a line, use components or a scale vector diagram.

Field theory gives you a useful shared language. Gravitational, electric and magnetic fields are physically different, but we describe them using field strength, field lines, potential and energy. The terminology lets you transfer ideas from one field to another without pretending that the underlying causes are identical.

Electric field lines and field-line density

An electric field line is an imaginary curve whose tangent gives the direction of the electric field at each point. The arrow on the line shows the direction of the force on a positive test charge.

Use these conventions when sketching and interpreting electric field lines:

• field lines leave positive charge and enter negative charge
• field lines never cross, because the field cannot have two directions at one point
• closer field lines represent a stronger electric field
• field lines meet conducting surfaces at 90°
• for a radial field, the lines spread out with distance, showing that the field weakens.

For a single point charge, the field is radial: outward for +Q, inward for −Q. For two like charges, field lines do not connect one charge to the other and there may be a zero-field point between them. For equal like charges, that point is halfway between them. For two unlike charges, field lines run from the positive charge to the negative charge.

You can map electric field patterns experimentally using small particles suspended in oil between shaped electrodes. A high potential difference makes the particles align with the field. This is a qualitative technique: you sketch the pattern, note where lines are denser, and compare it with the accepted field pattern. High-voltage supplies must be treated with care.

Fields near conductors and conducting spheres

A conductor is a material that contains mobile charge carriers able to move through it. In electrostatic equilibrium, surplus charge on a conductor lies on its outer surface. If there were a component of electric field along the surface, charges would move; therefore the electric field at a conducting surface is perpendicular to the surface.

For a single spherical conducting body, solid or hollow, the field outside is the same as if the total charge were concentrated at the centre of the sphere. The field outside is radial. Inside the conducting material, the electric field is zero. Inside a hollow conducting sphere, the field in the hollow interior is also zero, provided no charge is placed inside the cavity. This shielding behaviour is the idea behind a Faraday cage.

Uniform field between parallel plates

A uniform electric field is an electric field with the same magnitude and direction throughout a region. Between two large, oppositely charged parallel plates, the field is approximately uniform away from the edges: straight, parallel, equally spaced lines from the positive plate to the negative plate.

Near the edges, the field is not uniform. Edge effects are the weakening and curving of the field near the ends of the plates, where field lines spread out into the surrounding space. In IB sketches, show the central field as straight and equally spaced, and show the edge field curving outward rather than stopping suddenly.

For parallel plates,

E = V / d, where V is the potential difference between the plates (V), and d is the plate separation (m). This gives an equivalent unit for electric field strength: V m⁻¹. So N C⁻¹ and V m⁻¹ are the same physical unit in different clothing.

The force on a charge in an electric field is

F = qE.

Work done by an electric field or by an external force in moving a charge through a potential difference is often found from

W = qV, where W is work done or energy transferred (J).

The electronvolt is an energy unit equal to the energy transferred when a charge of magnitude one elementary charge moves through a potential difference of one volt. Numerically, 1 eV = 1.602176634 × 10⁻¹⁹ J. Work done in electric fields may therefore be given in joules or electronvolts; joules are SI, electronvolts are convenient for individual particles.

Magnetic field lines

A magnetic field is a region in which a magnetic pole, magnet or moving charge experiences a magnetic force. A magnetic field line is an imaginary curve whose tangent gives the direction in which a north-seeking pole would tend to move.

Magnetic field-line rules are similar to electric ones, with one crucial difference: magnetic field lines form closed loops. Outside a bar magnet they are drawn from the north-seeking pole to the south-seeking pole; inside the magnet the loop continues back from south to north. The lines never cross, and a greater density of lines represents a stronger magnetic field.

For a bar magnet, the field is densest near the poles. Unlike poles close together produce field lines linking across the gap, showing attraction. Like poles close together produce a region between them where fields oppose; for equal magnets there is a null point on the symmetry line.

Magnetic field patterns in this topic are restricted to a bar magnet, a current-carrying straight wire, a current-carrying circular coil and an air-core solenoid. Iron filings can show the shape of the field, but they do not show direction. A plotting compass gives direction because its north-seeking end aligns with the local magnetic field.

For a long straight current-carrying wire, the magnetic field lines are circles centred on the wire. Use the right-hand grip rule: point the thumb of your right hand in the direction of conventional current, and your curled fingers show the direction of the magnetic field lines. The field line spacing increases farther from the wire, so the magnetic field becomes weaker with distance.

For a circular coil, the field through the centre resembles the field of a short bar magnet. Looking at one face of the coil, anticlockwise conventional current makes that face north-seeking; clockwise current makes it south-seeking. Increasing the current or the number of turns strengthens the field.

An air-core solenoid is a long coil with no magnetic core. Its field pattern is like that of a bar magnet: nearly uniform and strong inside the solenoid, weaker and spreading outside. The field is strengthened by increasing current or turns per unit length. Adding an iron core would strengthen it further, but the restricted syllabus pattern here is the air-core solenoid.

The four fundamental interactions are gravitational, electromagnetic, weak nuclear and strong nuclear. Electric and magnetic effects are parts of the electromagnetic interaction, which is vastly stronger than gravity at particle scales and has infinite range. Moving charges produce magnetic fields, and moving charges in magnetic fields can be forced into curved paths; that is the doorway to particle accelerators and probes of matter in later topics.

Four fundamental interactions compared by strength and range.