All Questions — Every PYQ on One Page

State and prove Gauss's theorem in electrostatics. Write its differential form.

What do you mean by electric flux? What is the flux through a closed surface enclosing an electric dipole?

Using Gauss's law, find the field of a uniformly charged solid sphere outside and inside. Show the graphical variation and prove the field is zero inside (at the centre).

Calculate the electric field on the surface of a $^{238}_{92}$U nucleus (radius $7\times 10^{-15}$ m). Take $\varepsilon_0 = 8.85\times 10^{-12}$ C²/N·m², $e = 1.6\times 10^{-19}$ C.

Using Gauss's theorem, find the electric field intensity at a point due to a charged cylinder (long line of charge).

Two charges $8\ \mu$C and $2\ \mu$C are placed 50 cm apart in air. At which point is the electric field intensity zero?

State Coulomb's theorem (Coulomb's law) in electrostatics.

Calculate the force with which two electrons at a distance of $1.1$ Å in the hydrogen atom repel each other. What is the nature of the electrostatic field energy?

What is an electric dipole? Define electric dipole moment.

Deduce the electric potential (and field) at any point $(r,\theta)$ due to an electric dipole.

Prove that the electrostatic field is conservative.

Prove that the energy stored in a capacitor of capacitance $C$ is $\tfrac{1}{2}CV^2$, where $V$ is the potential.

Show that the capacitance of a parallel-plate capacitor is $C = \varepsilon_0 A/d$. What changes if a slab of dielectric constant $K$ is introduced?

Find the energy stored in a capacitor of capacitance 2 pF with potential 1 kV.

An air-filled parallel-plate capacitor has capacitance $C$. What will it be if immersed half in oil of dielectric constant 1.6?

Capacitance of a spherical capacitor: two concentric metallic spheres, outer earthed. (2018: diameters 20 cm and 30 cm.)

Find the capacitance per unit length of a cylindrical capacitor, the outer cylinder being earthed.

Two capacitors $C_1, C_2$ charged to potentials $V_1, V_2$ are connected together. Calculate the loss of energy on sharing of charges.

Write the relation between $\vec{D}$, $\vec{P}$ and $\vec{E}$ in a dielectric; define them and show $\vec{D} = \varepsilon_0\vec{E} + \vec{P}$.

What do you mean by polarization of a dielectric medium? Define the polarization vector.

Show that the magnitude of polarization equals the surface density of induced (bound) charge.

Distinguish between polar and non-polar dielectrics. Give examples.

Show that the electric field decreases when a dielectric slab is introduced between the plates of a capacitor.

State Biot–Savart's law in magnetostatics.

Find the magnetic induction at distance $r$ from a long straight conductor carrying current $I$. (2023 numeric: $I = 1.5$ A, $r = 3$ cm.)

Applying Biot–Savart's law, derive $\vec{B}$ at a point on the axis of a current-carrying circular loop.

Two parallel wires P and Q are $2r$ apart, carrying currents $i$ and $3i$ in the same direction. Find the point between the wires where the magnetic field is zero.

What is magnetic vector potential? (2018 adds three numerics: given $\vec{A}$, calculate $\vec{B}$.)

State Ampère's circuital law; mathematical form / show $\nabla\times\vec{B} = \mu_0\vec{J}$.

What is the meaning of $\nabla\cdot\vec{B} = 0$? Using Biot–Savart law prove $\nabla\cdot\vec{B} = 0$.

State (and explain) Faraday's laws of electromagnetic induction.

Write down the integral and differential forms of Faraday's law.

What do you mean by non-inductive coil?

Define self induction. Why is it called electric inertia?

Define coefficients of self and mutual inductance.

A coil of 800 turns has self-inductance 400 mH. What will be the self-inductance of a similar coil with 500 turns?

Solenoid 1 m long, 10 cm diameter, 5000 turns: (i) inductance, (ii) energy stored with 2 A current.

Find the self-inductance of a solenoid 40 cm long and radius 4 cm having 200 turns ($\mu_r = 1$).

Show that the equivalent inductance of two coils $L_1$, $L_2$ in parallel is $(L_1 L_2 − M^2)/(L_1 + L_2 − 2M)$.

Coils of 50 mH and 100 mH in series give effective inductance 75 mH. Determine the coefficient of mutual inductance.

Find the magnetic energy stored in an inductor of self-inductance $L$ carrying current $i$.

Define mutual induction. Calculate the mutual inductance of two coils wound on a cylinder of length $l$, cross-section $A$, with $N_1$ and $N_2$ turns respectively.

What do you mean by conduction current and displacement current?

Alternating emf $E = E_0\cos\omega t$ of frequency $10^{15}$ Hz applied to a conductor ($\sigma = 10^7$ mho/m). Ratio of conduction to displacement current?

Can we apply Ampere's law for non-steady currents? What is Maxwell's correction in this context?

Write down Maxwell's equations (free space / with symbols / inside material / with Maxwell's modification of Ampère's law).

From Maxwell's equations derive the EM wave equation in free space; express the speed in terms of $\varepsilon_0$ and $\mu_0$.

Define Poynting vector (and its unit).

Refractive index & velocity of light in a medium: velocity/wavelength in water ($n = 1.33$) and glass ($n = 1.658$) for $\lambda = 5893$ Å.

Write down the main properties of electromagnetic waves.

Show that $\vec{E} = E_0\cos(ky-\omega t)\,\hat{k}$ and $\vec{B} = B_0\cos(ky-\omega t)\,\hat{\imath}$ represent an electromagnetic field.

Find the resultant amplitude and phase due to superposition of $y_1 = 3\sin(50\pi t)$ cm and $y_2 = \sqrt{3}\cos(50\pi t)$ cm.

What are beats? How are they applied in the determination of poisonous gases in mines?

Sonometer numerical: tensions in ratio $8:1$, lengths $36:35$, diameters $4:1$, densities $1:2$; higher pitch $360$ Hz. Find beats produced.

What are beats? Give the theory of beats.

Two waves $y_1 = 3\sin(\omega t)$ and $y_2 = 4\sin(\omega t + \pi/6)$ superpose each other. What will be the amplitude of the resultant wave?

Two S.H.Ms of same frequency along the same line have amplitudes in the ratio $3:4$. If the phase difference between them is $45°$, find the ratio of the amplitude of the resultant S.H.M. to that of the smaller of the two.

What are Lissajous figures? (two practical applications / demonstration by electrical experiment)

Two SHMs of same frequency and amplitude, phase difference $\pi/2$, in perpendicular directions. What is the shape of the resultant motion?

Find the resultant of two perpendicular simple harmonic vibrations and discuss Lissajous figures.

What happens when two perpendicular vibrations of slightly different time periods are superimposed on a particle?

What are Lissajous figures? Show one such figure where ratio of frequencies is $1:2$.

State (and explain) Huygens' principle. (2024 couples it with "dual character of light" — that half is NOT in your syllabus)

What is interference of light? State the fundamental conditions for a steady observable interference pattern.

"Two separate sources of light cannot produce interference of light" — explain.

Young's double slit experiment: coherent waves, resultant intensity pattern, conditions of maxima and minima (both phase and path), and the intensity distribution plot.

State the conditions for a steady interference pattern. Find the fringe width in YDSE and prove that the dark and bright bands are of equal width.

What are constructive and destructive interference? Does destructive interference violate the law of conservation of energy?

In YDSE the slit separation $d = 0.1$ mm, the fringe width $\beta = 5$ mm, and the screen distance $D = 1$ m. Find the wavelength $\lambda$.

In YDSE a glass plate ($\mu_g = 1.5$, thickness $t_g = 12\times 10^{-5}$ mm) is placed over one slit and a diamond plate ($\mu_d = 2.5$) over the other. The central fringe does not shift. Find the thickness of the diamond plate.

What is meant by interference fringes? Give the theory of interference fringes.

In Young's double slit experiment, the screen is placed 2 m from the two sources separated by 1.5 mm. The interference fringes are obtained with monochromatic source of wavelength 6000 Å. Find the fringe width.

Write down the characteristics of Newton's rings.

Explain the formation of Newton's rings. Deduce the expression for the diameter (radius) of the $n$-th bright and dark ring by reflection in an air film.

In Newton's rings $R = 100$ cm; the diameter of the 3rd ring is $0.181$ cm and the diameter of the 13th ring is $0.501$ cm. Find the wavelength of light used.

Describe Newton's ring method to determine the wavelength of light.

In Newton's rings experiment, the diameters of 5th and 15th rings are 0.336 cm and 0.590 cm respectively. Find the radius of curvature of the plano-convex lens if the wavelength of light is 5890 Å.

In Newton's rings experiment, the diameter of the 4th dark ring is 0.4 cm and that of the 12th dark ring is 0.7 cm. Find the wavelength of incident light, if the radius of curvature of the plano-convex lens is 0.5 m.

With the help of Fresnel's bi-prism explain how an interference pattern is formed. How is the wavelength of light measured using a biprism?

A biprism is placed $5$ cm from a slit; the virtual images of the slit formed by the biprism are $0.05$ cm apart. The screen is placed $75$ cm from the biprism. Given $\lambda = 5.89\times 10^{-5}$ cm, find the fringe width.

What is the purpose of using biprism in interference experiment?

In Fresnel's biprism experiment, the fringe width is found to be 0.4 mm. If the distance of the biprism from the source is 20 cm and that of the screen is 80 cm, find the distance between the virtual images. Given wavelength of light used is 5890 Å.

In Fresnel's biprism experiment, the fringe width was found to be 0.6 mm. If the distance of the source from the biprism is 20 cm and that of the screen from the biprism is 80 cm, find the distance between the virtual sources. Given wavelength of light used is 5890 Å.

In Fresnel's biprism experiment, the fringe width was found to be 0.8 mm. If the distance of the source from the biprism is 30 cm and that of the screen from the biprism is 100 cm, find the distance between the virtual sources. Given wavelength of light used is 5890 Å.

Distinguish between Lloyd's mirror and Fresnel's biprism.

In Lloyd's mirror experiment, the real and virtual sources are 1 mm apart and the screen is placed at a distance of 1 m from the source. If the wavelength of light used is 5890 Å, find the fringe width.

In Lloyd's mirror experiment, the real and virtual sources are 1.5 mm apart and the screen is placed at a distance of 1.5 m from the source. If the wavelength of light used is 5890 Å, find the fringe width.

In Lloyd's mirror experiment, the real and virtual sources are 1.2 mm apart and the screen is placed at a distance of 1.2 m from the source. If the wavelength of light used is 5890 Å, find the fringe width.

Explain the formation of interference fringes due to a thin film when observed in reflected light.

Discuss Stokes' treatment of phase change on reflection.

What are Haidinger fringes? Explain the formation of these fringes.

Explain the formation of Fizeau fringes.

A soap film of refractive index 1.333 and thickness 5×10⁻⁷ m is observed at an angle of incidence of 40°. Find the wavelength of light in the visible spectrum which will be strongly reflected.

Explain the phenomenon of interference in thin films.

What is a zone plate? Explain its construction. Compare it with a convex lens.

What is a plane diffraction grating? Define grating element (grating constant). Describe the method of determining the wavelength of monochromatic light using a grating and a spectrometer.

Find the highest order of the spectrum with sodium light, given (i) $\lambda = 5.89\times 10^{-5}$ cm and $3000$ lines/cm (2022); (ii) $\lambda = 5896$ Å and $2000$ lines/cm (2023).

In a plane transmission grating the wavelength of light is $500$ nm and the second-order principal maximum is obtained at $30^\circ$. Find the number of lines per cm on the grating.

What is the difference between polarised and unpolarised light? How do you test it?

What is meant by double refraction of light? Name a double refracting crystal.

Write Huygens' theory of double refraction.

Find the thickness of a quarter-wave plate for sodium light λ = 589.6 nm with μ_o = 1.544, μ_e = 1.553.

Find the thickness of a quartz quarter-wave plate for λ = 5.9 × 10⁻⁵ cm with μ_o = 1.544, μ_e = 1.535.

How will you prepare elliptically and circularly polarized light using a Nicol prism and a quarter-wave plate? How do you test them?