Physics GRE GR 1777, Problem 021 Solution

21. Electrodynamics (Cyclotron) Solution The cyclotron frequency is the frequency of a charged particle moving perpendicular to the direction of a constant magnetic field B. Since the motion of a charged particle in the cyclotron is circular (because of a uniform magnetic field), we can calculate the cyclotron frequency by using the fact that the…

Physics GRE GR 1777, Problem 020 Solution

20. Electrodynamics (Magnetic field) Solution The magnitude of the magnetic field can be obtained from the Biot-Savart law. where is the radius of the loop and is the current. In this problem, the radius of the circular loop is , the magnitude of the magnetic field at the center of a circular loop is Answer…

Physics GRE GR 1777, Problem 019 Solution

19. Classical Mechanics (Work-Energy Principle) Solution From the work-energy theorem, Since the work done by the box is and the change of the kinetic energy is Therefore, The force is Answer (C) 3N Reference https://en.wikipedia.org/wiki/Work_(physics)#Work–energy_principle

GRE GR 1777, Problem 018 Solution

18. Classical Mechanics (Angular Momentum) Solution Angular momentum in circular motion is where is angular momentum, is the mass of the satellite, is the velocity, and is the orbital radius. In this problem, two satellites are identical. So the mass of the satellite is equal. The orbital radius of A is the ratio of the…

GRE GR 1777, Problem 017 Solution

17. Classical Mechanics (Stellar Dynamics) Solution In Keplar’s Thrid law, the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. where is the orbital period, and is the semi-major axis of the planet. For system 1 the radius of the orbit is , and…

GRE GR 1777, Problem 016 Solution

16. Optics (Electromagnetics) This problem asks the application of the Fermat’s principle of ray optics to another optics laws. Solution This principle shows the path of the light, so it can also be used to explain reflection and refraction of the light. So we can derive the Snell’s law and the law of reflection from…

GRE GR 1777, Problem 014 Solution

Physics GRE GR 1777 Quantum Mechanics (Planck length) + Dimensional analysis Solution 1) If you don’t know the Planck length, that’s fine. This question asks that you know about the dimensional analysis. The unit of the length should be . To find the proper expression for length, we construct the equation like this: The dimensions…

GRE GR 1777, Problem 013 Solution

Physics GRE GR 1777 13. Quantum Mechanics (Infinity potential wall) Infinity potential wall problem is one of the basic problems in quantum mechanics. So I recommend you to remember some equation about it. The energy eigenvalues of a particle of mass inside a one-dimensional box are . And the boundary condition () implies that where…

GRE GR 1777, Problem 012 Solution

Physics GRE GR 1777 Quantum Mechanics (Quantum number) The magnetic quantum number can be determined as Thus, the number of allowed values of is . Therefore, when , the number of allowed values of is 5. The answer is (E). References) https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Quantum_Mechanics/10%3A_Multi-electron_Atoms/Quantum_Numbers https://en.wikipedia.org/wiki/Magnetic_quantum_number

GRE GR 1777, Problem 011 Solution

Physics GRE GR 1777 11. Quantum Mechanics (Characteristic X-rays) By definition in the Wikipedia, characteristic X-rays are emitted when outer-shell electrons fill a vacancy in the inner shell of an atom, releasing X-rays in a pattern that is “characteristic” to each element. Therefore, the answer is (C). Tips) Actually, I didn’t see this in my…