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?

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.

Potential $V(x,y,z) = -k(x^2+y^2+z^2)$, $k$ a constant. Find $\vec{E}$ at $(1,1,1)$.

Find $\nabla\phi$ where $\phi = 1/r$.

Find the potential at $(x,y,z)$ for the conservative field $\vec{F} = (2xy+z^2)\hat{i} + x^2\hat{j} + 2xz\hat{k}$.

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.

What is magnetic vector potential? (2018 adds: 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 $i$.

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 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?

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.

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.

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 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? 2018

What is meant by double refraction of light? Name a double refracting crystal. 2022

Write Huygens' theory of double refraction. 2023

Find the thickness of a quarter-wave plate for sodium light λ = 589.6 nm with μ_o = 1.544, μ_e = 1.553. 2024

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. 2022

How will you prepare elliptically and circularly polarized light using a Nicol prism and a quarter-wave plate? How do you test them? 2019

Dipole torque numeric: length 3 cm, charges $5\,\mu$C, $E = 2\times 10^4$ N/C → max and min torque.

Explain what happens when an electric dipole is placed in a uniform electric field.

Dipole ($+1\,\mu$C, $-1\,\mu$C, 2 cm) in field $2.5\times 10^4$ N/C → torque to rotate it by 30°.

Lorentz force numeric: $q = 1.6\times 10^{-19}$ C, $\vec{v} = 3\hat{i}+2\hat{j}$ m/s, $\vec{E} = 6\hat{i}+6\hat{j}+3\hat{k}$ V/m, $\vec{B} = \hat{j}+2\hat{k}$ T.

What is the work done by a magnetic field on a moving charge?

Force between two parallel wires (10 cm long, 2 cm apart, currents 20 A and 30 A).

Parallel-plate capacitor ($A = 0.25$ m², $d = 1$ cm, 10 V battery) → force of attraction between plates.

What is meant by visibility of interference fringes? Two waves of amplitudes $2$ cm and $1$ cm interfere. Find the visibility.

State the resolving power of a plane diffraction grating. Show that $R = Nn$.

What do you mean by resolving power of an optical instrument?

What do you mean by optical activity?