Electricity, Magnetism & Optics – Preparatory Year Physics

A comprehensive set of question-and-answer flashcards covering core definitions, equations, and principles from electrostatics, Gauss’s law, electric potential, capacitors, DC circuits, magnetostatics, electromagnetic induction, and supporting laboratory concepts for preparatory-year engineering physics.

What law states that electric charge can neither be created nor destroyed, only transferred?

Law of conservation of charge

According to Coulomb’s Law, how does the electric force between two point charges depend on their separation distance?

It is inversely proportional to the square of the distance between them (F ∝ 1/r²).

Write the mathematical form of Coulomb’s Law in SI units.

F = ke |q₁q₂| / r², where ke = 8.99×10⁹ N·m²/C²

What is the value of the permittivity of free space (ε₀)?

ε₀ = 8.854 × 10⁻¹² C²/(N·m²)

Define electric field (vector form).

𝐄⃗ = 𝐅⃗ /q (force per unit positive test charge)

Give the magnitude of the electric field produced by a single point charge.

|E| = k_e |q| / r²

State Gauss’s Law in words.

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

Provide the integral form of Gauss’s Law.

∮ 𝐄⃗ · d𝐀⃗ = Q_enclosed / ε₀

For an infinite line of charge with linear density λ, what is the magnitude of the electric field at radial distance r?

E = λ/(2π ε₀ r)

Write the capacitance of a parallel-plate capacitor with vacuum between plates.

C = ε₀ A / d

How does inserting a dielectric with constant κ affect a capacitor’s capacitance?

Capacitance increases to C = κC₀ (κ > 1 for dielectrics).

Give the expression for energy stored in a charged capacitor.

U = ½ C (ΔV)² = ½ QΔV = Q²/(2C)

State Ohm’s Law.

V = IR

What is the SI unit of resistivity (ρ)?

Ohm-metre (Ω·m)

Describe how resistance of a conductor depends on temperature (linear approximation).

R = R₀[1 + α(T − T₀)] where α is the temperature coefficient.

Define electromotive force (emf).

The maximum potential difference a source can provide between its terminals.

Write the loop rule (Kirchhoff).

The algebraic sum of potential differences around any closed loop is zero.

What is the time constant for an RC circuit?

τ = RC

Express charge on a capacitor during charging in an RC circuit.

q(t) = Cε (1 − e^(−t/RC))

Express current during discharge of a capacitor through R.

I(t) = (Q_i / R) e^(−t/RC) (direction opposite previous charging current)

Give the magnetic force on a moving charge.

𝐅⃗ = q 𝐯⃗ × 𝐁⃗

What is the SI unit of magnetic field?

Tesla (T) where 1 T = 1 N·s/(C·m) = 10⁴ Gauss

Define the Lorentz force.

Total force on a charge in electric and magnetic fields: 𝐅⃗ = q(𝐄⃗ + 𝐯⃗ × 𝐁⃗).

Provide the radius of circular motion for a charge q with speed v in a perpendicular magnetic field B.

r = m v / (|q| B)

What is cyclotron frequency?

f = |q|B / (2πm)

State Biot–Savart Law for a current element.

d𝐁⃗ = (μ₀ / 4π) (I d𝐬⃗ × 𝑟̂) / r²

Magnetic field at distance r from a long straight current I.

B = μ₀ I / (2π r)

Magnetic field at centre of a N-turn circular loop of radius R carrying current I.

B = μ₀ N I / (2R)

Write Ampère’s Circuital Law.

∮ 𝐁⃗ · d𝐬⃗ = μ₀ I_enclosed

Magnetic field inside a long solenoid (n turns per unit length, current I).

B = μ₀ n I (approximately uniform)

Torque on a current loop of area A and current I in magnetic field B.

τ = N I A B sinθ = 𝐦⃗ × 𝐁⃗, where 𝐦⃗ = N I A 𝐧̂

State Faraday’s Law of electromagnetic induction.

Induced emf equals the negative time rate of change of magnetic flux: ε = −dΦ_B/dt.

What does Lenz’s Law predict?

The induced current opposes the change in magnetic flux that produces it (sign of Faraday’s law).

Give the motional emf generated in a rod of length ℓ moving with speed v perpendicular to magnetic field B.

ε = B ℓ v

Define magnetic flux Φ_B through area A.

Φ_B = ∫ 𝐁⃗ · d𝐀⃗ = B A cosθ for uniform fields

State Gauss’s Law for magnetism.

The net magnetic flux through any closed surface is zero: ∮ 𝐁⃗ · d𝐀⃗ = 0 (no magnetic monopoles).

Condition for velocity selector using crossed E and B fields.

Particles with speed v = E / B pass undeflected.

Expression for Hall voltage (thin plate of thickness t, carrying current I in field B).

V_H = (I B)/(n q t)

What is relative permeability (μ_r) of a material?

μ_r = μ / μ₀; indicates how a material responds to magnetic fields.

Differentiate paramagnetic, diamagnetic and ferromagnetic materials in terms of μ_r.

Paramagnetic: μr > 1 slightly; Diamagnetic: μr < 1 slightly; Ferromagnetic: μ_r ≫ 1 (hundreds to thousands).

Capacitance of a cylindrical capacitor (length L, radii a inner, b outer).

C = (2π ε₀ L) / ln(b/a)

State the equivalent capacitance for capacitors in parallel.

C_eq = C₁ + C₂ + …

State the equivalent capacitance for capacitors in series.

1/C_eq = 1/C₁ + 1/C₂ + …

Power delivered to a resistor in terms of current and resistance.

P = I² R = V² / R = I V

What is the magnetic force per unit length between two parallel wires carrying currents I₁ and I₂ separated by distance a?

F/L = μ₀ I₁ I₂ / (2π a) (attractive if currents same direction, repulsive if opposite)

Official definition of the ampere based on magnetic force.

Current that, in two parallel conductors 1-m apart in vacuum, produces 2×10⁻⁷ N/m force between them.

Time constant τ meaning in RC circuit charging.

Time at which charge (or voltage) reaches 63% of its final value or decays to 37% during discharge.

Formula for magnetic dipole moment of N-turn coil.

μ = N I A (vector normal to coil by right-hand rule)

Expression for electric potential of a point charge.

V = k_e q / r (zero at infinity)

Relationship between electric field and potential in differential form.

𝐄⃗ = −∇V

Electron volt (eV) definition.

Energy gained by an electron accelerated through 1 volt = 1.602 × 10⁻¹⁹ J

Drift velocity formula for charge carriers.

v_d = I / (n q A)

Magnetic field inside a toroid of N turns carrying current I at radius r.

B = μ₀ N I /(2π r) (inside only)

Equation for resistivity dependence on temperature.

ρ = ρ₀ [1 + α (T − T₀)]

Value of μ₀ (permeability of free space).

μ₀ = 4π × 10⁻⁷ T·m/A

What is displacement current conceptually? (though not detailed here)

A term added by Maxwell representing changing electric flux that produces magnetic fields like conduction current.

Describe Wheatstone bridge balance condition.

R₁/R₂ = R₃/Rₓ when galvanometer shows zero deflection.

Purpose of ground-fault circuit interrupter (GFCI).

Detects difference in currents in live and neutral wires; opens circuit if imbalance indicates leakage to ground.

Formula for induced emf in N-turn coil with changing area or angle.

ε = −N d/dt (B A cosθ)

Torque on current loop is maximum when the plane of the loop is to magnetic field.

Parallel (normal is perpendicular), giving sinθ = 1.