Electric Charges and Fields - Chapter 1

Vocabulary flashcards covering key concepts from the lecture notes on Electric Charges and Fields.

Static electricity

Charges produced by friction that accumulate on insulating surfaces and remain stationary until discharged; studied by electrostatics.

Electrostatics

The study of forces, fields, and potentials arising from static charges.

Electric charge

A property of matter with two signs (positive or negative); can be transferred, adds algebraically, and is conserved in isolated systems.

Polarity of charge

The distinguishing feature between the two kinds of charges (positive and negative).

Positive charge

Charge conventionally assigned to glass rod or cat’s fur after rubbing; by convention, glass/fur carries +e.

Negative charge

Charge conventionally assigned to plastic rod or silk after rubbing; by convention, plastic/silk carries −e.

Conductor

A material through which electric charges move easily (e.g., metals, earth).

Insulator

A material that resists movement of charge; charges remain localized (e.g., glass, porcelain, plastic, nylon).

Semiconductors

Materials with resistance to charge movement between conductors and insulators.

Additivity of charges

The total charge of a system is the algebraic sum of all individual charges.

Conservation of charge

In an isolated system, the total charge remains constant over time.

Quantisation of charge

Free charges occur in integral multiples of the elementary charge e (q = n e).

Elementary charge e

Magnitude of the charge on a proton or electron: e = 1.602 × 10^−19 C.

Coulomb’s law

F = k q1 q2 / r^2 along the line joining two point charges; k = 1/(4π ε0) ≈ 9 × 10^9 N m^2/C^2.

Coulomb’s constant k

k = 1/(4π ε0) ≈ 9 × 10^9 N m^2/C^2.

Permittivity of free space ε0

ε0 = 8.854 × 10^−12 C^2 N^−1 m^−2.

Electric field

Force on a test charge per unit charge: E = F/q; units N/C; points away from positive charges and toward negative charges.

Source charge

The charge that produces the electric field in space.

Test charge

A small charge used to probe the electric field; ideally disturbs the source negligibly; E = F/q in the limit q → 0.

Superposition principle (electrostatics)

The net electric field (or force) from multiple charges is the vector sum of the fields (or forces) from each charge.

Electric field due to a point charge

E = (1/(4π ε0)) q / r^2 r̂; directed radially from the charge.

Field lines

Curves whose tangents indicate the direction of the electric field; density of lines represents field strength and lines generally do not cross.

Dipole

Two equal and opposite charges ±q separated by a distance 2a; defines a dipole moment.

Dipole moment p

A vector p = q × 2a along the line from −q to +q; magnitude p = q × 2a.

Dipole field on the axis

E_axis ≈ (1/(4π ε0)) (2p) / r^3 (for r ≫ a), along the dipole axis.

Dipole field in the equatorial plane

E_eq ≈ (1/(4π ε0)) (p) / r^3, directed opposite to the dipole moment when in the plane perpendicular to the axis.

Torque on a dipole in a uniform field

τ = p × E; tends to align the dipole with the external field.

Electric flux

Φ = ∮ E · dS; units N m^2/C; measures the number of field lines crossing a surface.

Gauss’s law

Flux through a closed surface equals the enclosed charge divided by ε0: Φ = q_enclosed/ε0.

Gaussian surface

A closed surface chosen to apply Gauss’s law for symmetric charge configurations.

Infinite line charge field

E = λ / (2π ε0 r) radial from the line (cylindrical symmetry).

Uniform plane sheet field

E = σ / (2 ε0) on each side of the plane, directed away from the plane if σ > 0.

Uniform spherical shell field (outside)

Outside the shell, E = (1/(4π ε0)) q / r^2; field is as if all charge were at the center.

Uniform spherical shell field (inside)

Inside the shell, E = 0 (for r < R).