Physics KP PMS Paper II 2025

(a) Write down Maxwell’s equations in differential form and briefly explain the physical significance of each equation. Explicitly show that the electric and magnetic fields can be expressed in terms of the scalar potential φ and vector potential A.

(04)

(b) Using Maxwell’s equations, explicitly show that scalar and vector potentials satisfy the wave equation under Lorentz gauge condition:

(10)

(c) Derive the modified (Maxwell) form of Ampere’s law in differential form.

(06)

(a) State the Biot-Savart law. Derive the mathematical expression for the magnetic field B produced by a small current element I ds at a point P located a distance r away and explain the direction of field using the right-hand rule.

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(b) Using the Biot-Savart law, derive an expression for the magnetic field B at a point P located on the central perpendicular axis of a circular current-carrying loop of radius R.

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(c) State the principle of conservation of electric charge and derive the equation of continuity in its differential form.

(04)

(a) For a series RLC circuit, derive the expressions for resonance frequency, current in the circuit and voltage across the inductor & capacitor at resonance.

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(b) An AM radio receiver is tuned to a station broadcasting at a carrier frequency of 1MHz. The receiver uses a super heterodyne system with an intermediate frequency (IF) of 455 kHz. Calculate the frequency of the local oscillator when it is tuned for high-side injection. If the tuning circuit uses an inductor of 10 μH, find the required capacitance to tune the desired station at 1 MHz.

(05)

(c) In a common emitter transistor circuit, the base current (I_B) is 50μA, and the collector current (I_C) is 5mA. Calculate the current gain (β) of the transistor. If the collector supply voltage is V_CC = 10 V and the collector resistor R_C = 2 kΩ, calculate the collector-emitter voltage (V_CE).

(05)

(a) Explain the construction and working of a pentode vacuum tube. Describe its static and dynamic characteristics.

(10)

(b) Explain the Common Base (CB) configuration of a transistor with a neat circuit diagram. Discuss its input and output characteristics; derive the relation between I_E, I_C, and I_B, and define the current gain (α).

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(c) A silicon diode (V_γ = 0.7 V) is connected in series with a resistor R = 1 kΩ to a DC supply of V_S = 10V. Calculate the current flowing through the diode. Determine the power dissipated by the diode. Assume the diode is ideal except for its forward voltage drop V_γ = 0.7 V.

(03)

(a) State the phenomenon of Compton scattering. Derive an expression for the change in wavelength (Compton shift) of a photon scattered through an angle θ by a free stationary electron.

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(b) Monochromatic light of wavelength λ = 400.0 nm is incident on a metal whose work function is φ = 2.20 eV. Calculate the photon energy E_photon (in J and eV) and the maximum speed v_max of the emitted electrons (in m/s).

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(c) State De Broglie’s hypothesis and derive the mathematical expression for the De Broglie wavelength associated with a moving particle. Explain the physical significance of this hypothesis.

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(a) Use Schrödinger wave equation and derive the ground state wavefunction for one dimensional harmonic oscillator.

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(b) State the Heisenberg’s uncertainty principle. If the position of an electron is Δx = 1.0 × 10^-10 m (atomic scale), then what would be the minimum uncertainty in its momentum?

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(c) State and explain Bohr’s theory of the hydrogen atom. Derive the expressions for the radius and energy of an electron in the n^th orbit.

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(a) What is beta decay and write its general form. Explain the types of beta decay with examples. Moreover, describe the role of neutrinos, the energy released (Q-value), and the conservation laws involved.

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(b) Explain the working of a mass spectrometer. Derive the expressions for the velocity of an ion, the radius of curvature of the ion’s path in a uniform magnetic field B and the formula for the mass-to-charge ratio.

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(c) In a nuclear reactor, 1 gram of Uranium-235 undergoes fission. If each fission releases 200 MeV, calculate power generated if all fission occurs in 10 minutes.

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(a) Explain the radioactive decay law and derive the half-life of a nucleus.

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(b) Write down the general nuclear reaction equation of alpha decay. Derive the expressions of the kinetic energy of the alpha particle in terms of Q-value and recoil energy of the daughter particle.

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(c) Write down all the fundamental leptons, antileptons, quarks, antiquarks and gauge bosons, and also specify the electric charge of each particle type.

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