COMEDK UGET Physics - Electromagnetism and Modern Physics Syllabus

Give the formulas for cells connected in series and in parallel.

Series: EMF = nε, internal resistance = nr, I = nε/(R + nr). Parallel (n identical cells): EMF = ε, internal resistance = r/n, I = ε/(R + r/n).

State Joule's law of heating and give the formula for heat produced.

Heat produced H = I²Rt = VIt = (V²/R)t. Heat is proportional to the square of current, resistance, and time. Power P = I²R = VI = V²/R.

State the right-hand thumb rule and the Biot-Savart law.

Right-hand thumb rule: if the thumb points along current, curled fingers give the direction of the magnetic field. Biot-Savart law: dB = (μ₀/4π)(I dl sinθ)/r², giving the field due to a current element.

Give the magnetic field at the center of a circular current loop and inside a long solenoid.

Center of circular loop (N turns): B = μ₀NI/(2R). Inside a long solenoid: B = μ₀nI, where n is turns per unit length.

State Ampere's circuital law and give the field around a long straight wire.

Ampere's law: ∮B·dl = μ₀I_enclosed. Field around a long straight wire: B = μ₀I/(2πr).

Give the force on a current-carrying conductor and on a moving charge in a magnetic field.

On a conductor: F = BIL sinθ (F = IL × B). On a moving charge: F = qvB sinθ (F = qv × B). The Lorentz force combines electric and magnetic: F = q(E + v × B).

What is the principle and expression for the cyclotron frequency?

A cyclotron accelerates charged particles using a perpendicular magnetic field and alternating electric field. The cyclotron frequency f = qB/(2πm) is independent of the particle's speed and radius. Maximum KE = q²B²r²/(2m).

Give the force per unit length between two parallel current-carrying wires.

F/L = μ₀I₁I₂/(2πd). Currents in the same direction attract; opposite directions repel. This defines the ampere.

Define magnetic dipole moment of a current loop and torque on it in a magnetic field.

Magnetic moment m = NIA (N turns, current I, area A). Torque τ = mB sinθ = m × B. Potential energy U = -m·B = -mB cosθ.

Distinguish between diamagnetic, paramagnetic, and ferromagnetic materials.

Diamagnetic: weakly repelled, relative permeability μᵣ < 1, susceptibility small negative (e.g., bismuth). Paramagnetic: weakly attracted, μᵣ slightly > 1, small positive susceptibility (e.g., aluminium). Ferromagnetic: strongly attracted, μᵣ >> 1, large positive susceptibility (e.g., iron).

Define magnetic susceptibility and its relation to relative permeability.

Magnetic susceptibility χ = M/H (magnetization per unit magnetizing field). Relation: μᵣ = 1 + χ, and permeability μ = μ₀(1 + χ).

State Curie's law for paramagnetic materials.

The magnetic susceptibility of a paramagnetic material is inversely proportional to absolute temperature: χ = C/T, where C is the Curie constant. Above the Curie temperature, ferromagnetics become paramagnetic.

State Faraday's laws of electromagnetic induction.

First law: an EMF is induced whenever magnetic flux through a circuit changes. Second law: the magnitude of induced EMF equals the rate of change of flux: ε = -dΦ/dt (for N turns, ε = -N dΦ/dt).

State Lenz's law and what conservation principle it represents.

The induced current opposes the change in magnetic flux that produces it (the negative sign in Faraday's law). It is a consequence of the conservation of energy.

Define self-inductance and mutual inductance.

Self-inductance L: EMF induced in a coil due to change in its own current, ε = -L(dI/dt); Φ = LI. Mutual inductance M: EMF induced in one coil due to changing current in a neighboring coil, ε₂ = -M(dI₁/dt). Unit: henry (H).

Give the expression for motional EMF.

When a rod of length L moves with velocity v perpendicular to a magnetic field B, the induced EMF is ε = BLv.

Define RMS value and peak value relationship for alternating current.

I_rms = I₀/√2 ≈ 0.707 I₀, and V_rms = V₀/√2, where I₀ and V₀ are peak values. RMS is the effective value producing the same heating as a DC current.

Define inductive and capacitive reactance in AC circuits.

Inductive reactance X_L = ωL = 2πfL (increases with frequency). Capacitive reactance X_C = 1/(ωC) = 1/(2πfC) (decreases with frequency). Both measured in ohms.

Give the impedance of a series LCR circuit and the resonance frequency.

Impedance Z = √[R² + (X_L - X_C)²]. Resonance occurs when X_L = X_C, giving f₀ = 1/(2π√(LC)), where Z is minimum (= R) and current is maximum.

Define power factor in an AC circuit.

Power factor = cosφ = R/Z, where φ is the phase angle between voltage and current. Average power P = V_rms·I_rms·cosφ. For a pure inductor or capacitor, cosφ = 0 (wattless current).

State the principle of a transformer and the turns ratio relation.

A transformer works on mutual induction, transferring AC power between coils. V_s/V_p = N_s/N_p = I_p/I_s. Step-up: N_s > N_p (increases voltage); step-down: N_s < N_p.

Give the order of frequency/wavelength of the electromagnetic spectrum from low to high frequency.

Increasing frequency (decreasing wavelength): radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.

What is the speed of electromagnetic waves in vacuum and its relation to ε₀ and μ₀?

c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s. EM waves are transverse, with E and B perpendicular to each other and to the direction of propagation, and E₀/B₀ = c.

State the laws of reflection and the mirror formula.

Laws of reflection: angle of incidence = angle of reflection; incident ray, reflected ray, and normal lie in one plane. Mirror formula: 1/v + 1/u = 1/f, where f = R/2. Magnification m = -v/u.

State Snell's law of refraction and define refractive index.

Snell's law: n₁ sinθ₁ = n₂ sinθ₂. Refractive index n = c/v = sin(i)/sin(r), the ratio of speed of light in vacuum to that in the medium.

Define critical angle and the condition for total internal reflection.

Critical angle C is the angle of incidence in the denser medium for which the refraction angle is 90°: sin C = 1/n. Total internal reflection occurs when light travels from denser to rarer medium and the angle of incidence exceeds C.

Give the lens maker's formula and the lens formula.

Lens maker's formula: 1/f = (n-1)(1/R₁ - 1/R₂). Lens formula: 1/v - 1/u = 1/f. Power P = 1/f (in metres), measured in dioptres (D). Magnification m = v/u.

State Huygens' principle and the conditions for constructive/destructive interference.

Huygens' principle: every point on a wavefront acts as a source of secondary wavelets; the new wavefront is their envelope. Constructive interference: path difference = nλ. Destructive: path difference = (n + ½)λ.

Give the fringe width formula in Young's double-slit experiment.

Fringe width β = λD/d, where λ is wavelength, D the slit-to-screen distance, and d the slit separation. Bright fringes at path difference nλ; dark at (n + ½)λ.

What is dispersion of light and what causes it? Give the order of the spectrum.

Dispersion is the splitting of white light into its constituent colors by a prism, caused because refractive index depends on wavelength (violet bends most, red least). The spectrum order is VIBGYOR: violet, indigo, blue, green, yellow, orange, red.

State Rayleigh's law of scattering and explain why the sky is blue.

Intensity of scattered light is inversely proportional to the fourth power of wavelength: I ∝ 1/λ⁴. Blue light (shorter wavelength) scatters more than red, so the sky appears blue; the sun appears red at sunrise/sunset due to longer path scattering away the blue.

State Einstein's photoelectric equation and define work function.

KE_max = hν - φ₀, where hν is photon energy and φ₀ the work function (minimum energy to eject an electron). Threshold frequency ν₀ = φ₀/h. Stopping potential: eV₀ = KE_max.

Give the de Broglie wavelength formula for a moving particle.

λ = h/p = h/(mv) = h/√(2mKE). For an electron accelerated through potential V: λ = 12.27/√V Å. This expresses the wave nature of matter.

State Bohr's postulates for the hydrogen atom and give the energy of the nth level.

Electrons move in stationary orbits where angular momentum is quantized: mvr = nh/2π. Energy is radiated only on transition between orbits: hν = E₂ - E₁. Energy: Eₙ = -13.6/n² eV. Radius rₙ ∝ n².

What is the Rydberg formula for hydrogen spectral lines and name the series in the visible region?

1/λ = R(1/n₁² - 1/n₂²), where R = 1.097 × 10⁷ m⁻¹. The Balmer series (transitions to n = 2) lies in the visible region. Lyman series is UV; Paschen, Brackett are infrared.

Define mass defect and binding energy of a nucleus.

Mass defect Δm = (sum of nucleon masses) - (actual nuclear mass). Binding energy = Δm·c² (1 u = 931.5 MeV). Higher binding energy per nucleon means a more stable nucleus (maximum near iron, A ≈ 56).

Compare alpha, beta, and gamma radiations.

Alpha (α): helium nucleus (²₄He), positive charge, least penetrating, most ionizing. Beta (β): electron/positron, negative/positive, moderate penetration. Gamma (γ): high-energy EM photon, no charge, most penetrating, least ionizing.

State the law of radioactive decay and define half-life.

N = N₀e^(-λt), where λ is the decay constant. Half-life T₁/₂ = 0.693/λ is the time for half the nuclei to decay. Mean life τ = 1/λ. Activity A = λN.

Distinguish between nuclear fission and nuclear fusion.

Fission: a heavy nucleus splits into lighter nuclei releasing energy (e.g., U-235 in reactors/bombs). Fusion: light nuclei combine into a heavier one releasing energy (e.g., hydrogen to helium in the Sun); requires extremely high temperature.

Distinguish between intrinsic and extrinsic (n-type and p-type) semiconductors.

Intrinsic: pure semiconductor; equal electrons and holes. Extrinsic: doped. n-type doped with pentavalent impurity (electrons are majority carriers); p-type doped with trivalent impurity (holes are majority carriers).

Explain forward and reverse bias of a p-n junction diode and its use as a rectifier.

Forward bias: p connected to positive terminal; barrier reduced, large current flows. Reverse bias: p to negative; barrier increased, only tiny leakage current. A diode conducts in one direction, so it acts as a rectifier (half-wave uses one diode, full-wave uses two/four).