Electric Charge and Electric Field – Chapter 1 Review

These question-and-answer cards cover fundamental definitions, laws, formulas, and conceptual insights from Chapter 1 on Electric Charge and Electric Field, including Coulomb’s law, Gauss’s law, dipoles, field lines, and charge distributions.

What is the magnitude of the fundamental (minimum) charge on an electron or proton?

e = 1.6 × 10⁻¹⁹ C

State the quantization of charge equation.

Total charge Q on a body is Q = n e, where n = 0, ±1, ±2 …

In everyday (macroscopic) situations, why is charge quantization often ignored?

Because the charges involved are so large that the discrete steps of ±e are negligible.

Name two common methods of charging a body.

Friction (triboelectric effect) and induction.

When a glass rod is rubbed with silk, which object becomes positively charged and why?

The glass rod becomes +ve because it loses electrons to the silk.

State Coulomb’s law in scalar form for vacuum.

F = k |q₁q₂| / r², where k = 9 × 10⁹ N m² C⁻².

What is the expression for Coulomb’s constant k in terms of ε₀?

k = 1 / (4π ε₀).

Give the SI unit and symbol for permittivity of free space.

ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²

How does force between two charges change inside a dielectric medium?

Fmedium = Fvacuum / K, where K (or ε_r) is the dielectric constant (>1).

Write Coulomb’s law in vector form for force on q₂ due to q₁.

𝐅₂₁ = (1/4π ε₀) (q₁q₂ / r³) 𝐫̂₁₂, directed along the line joining q₁ to q₂.

What principle explains that multiple forces add vectorially on a charge?

Superposition Principle.

Define electric field intensity at a point.

𝐄 = 𝐅 / q₀, the force per unit positive test charge placed at that point.

Write the field due to a point charge Q at distance r.

E = k Q / r², directed radially outward if Q > 0 and inward if Q < 0.

List two characteristics of electric field lines.

They originate on +ve charges and terminate on –ve charges; two lines never intersect.

What is electric flux through a surface?

Φ = ∬ 𝐄 · d𝐀, scalar measure of field lines crossing the surface.

State Gauss’s law in words.

The net electric flux through any closed surface equals the enclosed charge divided by ε₀.

Write Gauss’s law in integral form.

∯ 𝐄 · d𝐀 = Q_enclosed / ε₀.

Define linear charge density and give its symbol.

λ = Q / L, charge per unit length (C m⁻¹).

Give the electric field magnitude at distance r from an infinitely long uniformly charged wire.

E = λ / (2π ε₀ r).

For an infinite plane sheet of charge with surface density σ, what is the electric field near the sheet?

E = σ / (2 ε₀), directed normal to the sheet.

Inside a uniformly charged hollow conducting sphere, what is the electric field?

E = 0 (field inside a conductor is zero).

Outside a uniformly charged spherical shell (radius R, total charge Q), what is the field at distance r (r>R)?

E = k Q / r², as if all charge were concentrated at the centre.

Define an electric dipole.

Two equal and opposite charges separated by a finite distance 2a.

What is the vector definition of electric dipole moment?

𝐩 = q (2a) 𝐧̂ from –q to +q.

Write the torque on an electric dipole in a uniform field.

τ = 𝐩 × 𝐄 = pE sinθ, tending to align 𝐩 with 𝐄.

For a dipole on its axial line (r ≫ a), give the electric field magnitude.

E_axial ≈ 2k p / r³.

For a dipole on its equatorial line (r ≫ a), give the electric field magnitude.

E_equatorial ≈ k p / r³, directed opposite to the dipole moment.

What is the relation between Eaxial and Eequatorial for a point dipole?

Eaxial = 2 Eequatorial.

State the law of conservation of charge.

Charge can neither be created nor destroyed; it can only be transferred within an isolated system.

When two identical charged conductors are connected, what quantity becomes equal?

Their charges redistribute to give equal charge (average); potentials were already equal because they are identical.

When two non-identical conductors are connected, what becomes equal after connection?

Their potentials become equal.

If a conductor is grounded, what potential does it acquire?

Zero potential (earth potential).

How many electrons must be removed to give a body a charge of +1 μC?

n = Q/e = (1 × 10⁻⁶ C) / (1.6 × 10⁻¹⁹ C) ≈ 6.25 × 10¹² electrons.

What is the expression for electric field inside a uniformly charged solid sphere (radius R) at distance r<R?

E = (k Q r) / R³ (directly proportional to r).

Give the standard SI unit for electric field.

Newton per Coulomb (N C⁻¹) or equivalently Volt per metre (V m⁻¹).

What is meant by relative permittivity (dielectric constant) ε_r?

ε_r = ε / ε₀; ratio of permittivity of a medium to that of free space.

Write the condition for stable equilibrium of a dipole in a uniform field.

θ = 0°, dipole moment parallel to field; torque is zero and stable.

Why do two electric field lines never cross?

Because a unique tangent (direction of E) must exist at every point; crossing would imply two directions at one point.

What happens to the electric flux through a closed surface if the enclosed charge is doubled?

Flux doubles; Φ ∝ Q_enclosed.

Give the expressions for surface and volume charge densities.

σ = Q/A (C m⁻²); ρ = Q/V (C m⁻³).

State the superposition formula for net force on charge q₁ due to n other charges.

𝐅₁ = Σ (1/4π ε₀) (q₁ q_j / r₁j²) 𝐫̂₁j for j = 2 to n.

Does Gauss’s law determine the electric field uniquely everywhere?

Only when high symmetry (spherical, cylindrical, planar) allows field to be taken constant on Gaussian surfaces.

What is the direction of electric field just outside a positively charged conductor?

Normal outward to the surface.

Explain why electric field inside a conductor is zero in electrostatic equilibrium.

Free charges rearrange until internal field cancels; otherwise charges would continue to move.