DISPLACEMENT CURRENT
Concept & Applications
- Describe briefly how the concept of displacement current is explained through charging/discharging of a capacitor in an electric circuit.
- How is displacement current produced between the plates of a parallel plate capacitor during charging?
- Distinguish between displacement current and conduction current.
- Show that the displacement current inside a capacitor is the same as the current charging it (AC source, plate area A, separation d).
- Explain using Ampere–Maxwell law why current flows through a capacitor when being charged by a battery. Write the displacement current in terms of rate of change of electric flux.
- Why does current not flow in steady state in a capacitor connected across a DC battery? Explain momentary current during charging/discharging.
- Write Maxwell’s generalization of Ampere’s circuital law and show that i = ε₀ dΦE/dt during charging of capacitor.
ELECTROMAGNETIC WAVES
Production & Nature
- How does an oscillating charge produce electromagnetic waves?
- Sketch a schematic diagram depicting oscillating electric and magnetic fields of an EM wave propagating along +z direction.
- How is the frequency of EM waves related to the frequency of the oscillating charge?
- Directions of electric and magnetic field vectors relative to each other and propagation.
- Express the velocity of propagation in terms of peak values of electric and magnetic fields.
- Prove that average energy density of electric field equals that of magnetic field.
- Show, by example, how EM waves carry energy and momentum.
- Determine propagation and magnetic field directions for E = E₀ sin(ωt + kz).
- Write two characteristics of electromagnetic waves.
- Explain why a galvanometer shows momentary deflection during charging/discharging of a capacitor.
- Explain production of microwaves and why their frequency matches resonant frequency of water molecules in ovens.
- Name types of EM radiation for (i) cancer treatment, (ii) tanning, (iii) maintaining Earth’s warmth, and method of producing any one.
- Case-based conceptual questions (brain tumor, values, radioisotopes, gamma-rays, treatment).
ELECTROMAGNETIC SPECTRUM
Waves & Applications
- Why are infrared waves referred to as heat waves?
- Name EM radiation also called heat waves.
- Identify EM waves for (i) killing germs in water purifiers, (ii) eye surgery, (iii) radar systems; write one source and one use each.
- Identify EM waves with minimum wavelength and minimum frequency; write one use of each.
- Distinguish gamma rays and radio waves in origin and application.
- Identify EM spectrum parts used in radar systems and eye surgery; write frequency ranges.
- If Earth had no atmosphere, would surface temperature be higher or lower? Explain.
- Explain how EM waves exert pressure on a surface.
- Explain how microwave ovens heat food containing water molecules.
- Arrange EM waves in ascending order of frequency: gamma rays, microwaves, infrared, ultraviolet.
MAGNETISM & MATTER
Fundamentals
- State Gauss’s law in magnetism. How is it different from Gauss’s law in electrostatics and why?
- Define magnetic dipole moment. Is it a scalar or vector quantity? Give its SI unit.
- Derive an expression for the potential energy of a magnetic dipole in a uniform magnetic field at angle θ. When is it in stable and unstable equilibrium?
- Show that a current-carrying solenoid behaves like a small bar magnet and compare its axial field with that of a bar magnet.
- Explain the SHM of a freely suspended magnetic dipole in a uniform magnetic field and derive the time period T = 2π√(I/mB).
- Deduce the expression for the magnetic dipole moment of an electron orbiting around the nucleus.
Magnetic Field Lines & Properties
- Draw magnetic field lines due to a circular loop carrying current. Show it acts as a bar magnet with m = IA.
- Write four important properties of magnetic field lines due to a bar magnet.
- Why can’t two magnetic field lines intersect each other?
- Why do magnetic field lines form continuous closed loops?
- Depict the field-line pattern of a current-carrying solenoid. How do these lines differ from an electric dipole?
Magnetism in Materials
- Define magnetising field, magnetic induction, intensity of magnetisation, magnetising field intensity, magnetic permeability, relative permeability, and magnetic susceptibility. Write relations among them.
- Describe properties of diamagnetic, paramagnetic, and ferromagnetic substances.
- Describe diamagnetism in superconducting metals.
- Draw field lines when (i) diamagnetic, (ii) paramagnetic substances are placed in an external field. Which property distinguishes this behaviour?
- Show diagrammatically field lines in paramagnetic and diamagnetic materials. Explain.
- Explain the basic difference between atom and molecule of diamagnetic vs paramagnetic materials.
- Why are elements with even atomic numbers more likely to be diamagnetic?
- Distinguish paramagnetic vs diamagnetic, and diamagnetic vs ferromagnetic in terms of susceptibility and behaviour in non-uniform fields.
Comparisons & Applications
- Distinguish properties of dia-, para-, and ferro-magnetic substances (susceptibility, permeability). Give one example for each.
- Draw and explain modifications in field lines for Nickel, Antimony, and Aluminium in a uniform magnetic field.
- Write three points of difference between para-, dia-, and ferro-magnetic materials with examples.
- Define magnetic susceptibility. Name one element with positive and one with negative susceptibility. What does negative susceptibility signify?
- Identify nature and susceptibility of materials given relative permeability or susceptibility values.
- Draw modifications in magnetic field pattern for paramagnetic and diamagnetic bars placed in uniform field.
- Explain behaviour of diamagnetic material when cooled and why paramagnetic sample shows greater magnetisation when cooled.
- Discuss temperature dependence of susceptibility for dia-, para-, and ferromagnetic materials.
- State Curie’s law and its modification for ferromagnetic substances.
WAVE OPTICS
Huygens’ Principle
- Define wavefront. How is it different from a ray?
- State Huygens’ principle.
- Depict wavefront shape for light diverging from a point source.
- Depict wavefront shape for light emerging from a convex lens with point source at focus.
- Show how plane wavefront traverses through a convex lens and focuses.
- Use Huygens’ construction to show plane wave reflection and verify law of reflection.
- Use Huygens’ principle to obtain law of refraction from rarer to denser and denser to rarer medium.
- Explain why reflected and refracted light have the same frequency.
- Explain effect of decreased speed in denser medium on energy of light.
Interference of Waves
- State conditions for coherent sources and why coherence is necessary for interference.
- Show that resultant intensity of two coherent waves depends on phase difference. Obtain conditions for constructive and destructive interference.
- In Young’s double slit experiment, explain formation of bright and dark fringes and factors affecting fringe width.
- Explain effects on interference fringes when (i) slit separation decreased, (ii) width of source slit increased, (iii) monochromatic source replaced by white light.
- Explain effect on fringe width if Young’s experiment is immersed in water.
Diffraction
- Use Huygens’ principle to explain formation of diffraction pattern from a single slit.
- Explain diffraction pattern formation using secondary wavelets on a screen.
- Write three features distinguishing interference fringes and single slit diffraction pattern.
- Explain why secondary maxima become weaker as order increases.
- Explain effect of slit width, screen distance, and wavelength on angular width of central maximum.
- Explain bright spot formation at center of shadow of a tiny circular obstacle.
ATOMS
Alpha Particle Scattering & Rutherford’s Nuclear Model
- State assumptions of Rutherford model. Why cannot it account for atomic stability?
- Draw Geiger–Marsden experiment setup and explain estimation of nuclear size.
- Explain why few α-particles scatter at angles > 90°. Give two conclusions about atomic structure.
- Write two limitations of Rutherford nuclear model.
- Derive expression for total energy of electron in hydrogen atom. Explain significance of negative energy.
Bohr Model of Hydrogen Atom
- Write two limitations of Rutherford model and explain Bohr's improvements.
- State postulates of Bohr’s hydrogen atom model.
- Write mathematical forms of three postulates of Bohr's theory.
- Derive radius of nth orbit and Bohr’s radius.
- Show circumference of nth orbit = n × de Broglie wavelength.
- How is necessary centripetal force provided for electron?
- Derive total energy expression; show K = –2U.
- Derive speed and time period of electron in nth orbit. Show time period ∝ n³.
- State Bohr postulate for emitted photon frequency. Derive expression for transition ni → nf.
- Show radius ∝ n² and total energy ∝ 1/n².
- Derive magnetic field at nucleus due to electron in ground state orbit.
Hydrogen Spectral Series
- Identify shortest and longest wavelengths in Lyman, Balmer, Paschen, Brackett & Pfund series and spectral regions.
- Maximum number of spectral lines emitted in third excited state.
- Conditions for obtaining Hα line in emission spectrum.
- Explain how electron transitions produce spectral series in hydrogen.
