所屬科目：研究所、轉學考(插大)◆普通物理學
1. In free space, there are two point charges of Q1= 2q and Q2 = 6q located at (0, 2r, r) and (r, 0, 3r) in rectangular (Cartesian) coordinate system. What is the magnitude of the force experienced by Q2?(A)(B)(C)(D)(E)None of the above
2. A sphere with radius a contains a uniform volume charge density ofρvin the region: 0 ＜ r ＜ a. If the sphere is isolated by a conducting spherical shell with inner radius b and outer radius c placed concentrically, as shown in figure. What is the electric field intensity in the region b ＜ r ＜ c?(A)(B)(C)(D)(E)None of the above
3. A straight wire carrying a current I in the z direction is located along the z axis in free space. If the wire is infinitely long and infinitely thin, what is the magnetic field intensity at the point (0, L, 0) in rectangular coordinate system?(A)(B)(C)(D)(E)None of the above
4. In a perfect dielectric medium with the permeability of \(\mu\), there exists an electric field given as \(\mathbf{E} = E0cos(ωt - kz)ax, where E0 is the peak value, \(\omega\) is the frequency, k is a constant, and \(\hat{a}_x\) is the unit vector in x direction. What is the magnetic field (H) in the region?(A)(B)0(C)(D)(E)None of the above
5. A uniform electromagnetic plane wave is traveling in free space and its electric field is given by E = 5cos(ωt-2z)ax V/m, what is the angular frequency, ω in (rad/s), of the plane wave?(A)3✖108(B)6✖108(C)6✖109(D)6.28✖108(E)None of the above
6. A long core-shell structure is made to transmit an optical wave through total internal reflection within the core region. If the refractive indices for the core and the shell are respectively n1 = 1.5 and n2 = 3.0, as depicted in the figure. What is the minimum value of the angle \(\theta\) for a successful transmission?(A)30°(B)45°(C)60°(D)90°(E)None of the above
7. An object is placed at the position being 20 cm from a convex lens with the focal length of 10 cm. What is the distance between the image and the lens?(A)20 cm(B)10 cm(C)40 cm(D)30 cm(E)None of the above
8. The spherical waves of wavelength \(\lambda\) emitted from a single point source are passing through two small holes, S1 and S2, which are separated by the distance of a, as shown in the figure. If c >> a, what is the approximated condition for destructive interference at a point P on the screen?(A)asinθ =1.5λ(B)asinθ =1.5λ(C)c sinθ=λ(D)b tanθ=λ(E)a sinθ =λ
9. A laser beam of wavelength \(\lambda\) shined on a spectrometer with the grating spacing a is split into two beams of wavelengthsλ1 and λ2 due to the 2nd order diffraction. If λ2 is slightly longer than λ1 and θ is the diffraction angle for \(\lambda_1\), what is the difference in diffraction angles of the two beams?(A)(B)(C)(D)(E)None of the above
10. A light beam is traveling in a structure with three layers of different refractive indices: n1 = 2,n2 =, n3 = 1. If the beam impinges at the interface between n1 and n2 with the incident angle of 60°, as shown in the figure, what is θwhen the light beam enters the layer with n3 = 1?(A)30°(B)45°(C)60°(D)90°(E)None of the above
11. A particle is strictly confined in a region of length L, but moving freely in the region. Two possible wavefunctions, φ1 andφ2, of the particle are those shown in the figure. When the particle is in the state corresponding to the wavefunction φ1， its total energy is 1 eV. What is its total energy in the state corresponding to φ2?(A)1 eV(B)2 eV(C)3 eV(D)4 eV(E)None of the above
12. An electron is trapped in an infinitely deep potential well with the width of 5 nm. When the electron is transferred from energy level E\(_2\) to E\(_1\), a photon of the wavelength 800 nm is emitted. If the width of the infinite well is increased to 10 nm, and the trapped electron is still transferred from E\(_2\) to E\(_1\), what can be the emitted photon wavelength?(A)200 nm(B)400 nm(C)1600 nm(D)3200 nm(E)None of the above
13. A copper ball of mass m and specific heat c is at a temperature T1 = 86.85°C. The ball is thrown into a large lake at T2 = 6.85°C, which stays constant. What is the total change in entropy of the copper ball and the lake?(A)(B)(C)(D)(E)None of the above
14. A particle is trapped in a potential well with the depth of E\(_0\). If the wavefunction of the particle is \(\psi(x,t) = A\sin(\omega t + kx) + iA\cos(\omega t + kx)\), where A, \(\omega\) and k are constants and i is the unit imaginary number, what is the probability, per unit length of the x axis, of finding the particle near the coordinate x at time t?(A)E0(B)A2(C)(D)A(E)None of the above
15. Two metal plates are connected to a battery and a current meter. When a light beam with tunable energy E is shined on one of the plates, the values read by the current meter is plotted as a function of E. E0 corresponds to the photon density of 1012cm-3and the photon wavelength of 200 nm. When the incident photon wavelength is increased to 400 nm, what is the photon density to obtain the current value of 5 μA?(A)2✖1012 cm-3(B)4✖1012 cm-3(C)8✖1022cm-3(D)1012-3(E)None of the above
16. Train A travels at 0.8c and passes a station platform. An observer on the platform records a time interval of 2 μs as the front and the rear of the train pass the observer. What is the proper length of the train?(A)288 m(B)320 m(C)480 m(D)600 m(E)None of the above
17. A container contains 2 moles of ideal monatomic gas with volume V0 and temperature T0. What is the change in entropy of the ideal gas if the container is compressed isothermally as its volume is reduced to exactly one half of the initial volume?(A)3R ln 2(B)-3Rln2(C)2Rln2(D)-2Rln2(E)None of the above
18. A 200 g ball is thrown at 30 m/s. It is struck by a bat which gives it a velocity of 40 m/s in the opposite direction. If the time of contact is 10-2s, what is the average force on the ball?(A)1000 N(B)1200 N(C)1400 N(D)1600 N(E)None of the above
19. A quarter circle with a linear density \(\lambda\) kg/m and a radius R as shown in the figure. What is the distance from the center of the quarter circle O to the center of mass of the quarter circle?(A)(B)0(C)(D)(E)None of the above
20. A particle of mass m1 = 2kg moving at velocity u (m/s) makes a one-dimensional elastic collision with a particle of mass m2 at rest. What is the possible mass of m2if it has one-third the initial kinetic energy of m1 after collision?(A)(B)(C)(D)(E)None of the above
21. A marble of radius r rolls without slipping down an incline and then up along a vertical circular track of radius R, as shown in the figure. What is the minimum height H from which the ball must start so that it barely stays in contact at the top of the circle? Assume r ＜＜ H and r ＜＜ R.(A)2 R(B)2.3 R(C)2.7 R(D)3 R(E)None of the above
22. Water emerges at speed \(v_0\) from the opening of a faucet of radius R. In laminar flow, the cross-sectional area of the vertical stream of water decreases as it falls. What is the relation between the radius r of the stream and the vertical drop y?(A)(B)(C)(D)(E)None of the above
23. What is the period T of the spring-block system for two springs with spring constants \(k_1\) and \(k_2\) respectively connected in series as shown in the figure? The mass of the block is m.(A)(B)(C)(D)(E)None of the above
24. A string of length L and linear mass density \(\lambda\) is under a tension F and vibrates in its fundamental mode at f1. What is the new fundamental frequency if the length L increases by 25%, the linear mass densityλdecreases by 20%, and the tension decreases by 20%?(A)1.2 f1(B)0.8 f1(C)0.83f1(D)1.25 f1(E)None of the above
25. An ideal monatomic gas undergoes an adiabatic process that the pressure and volume change from (P1, V1) to (P2, V2). What is the work done in this adiabatic process?(A)(B)(C)(D)(E)None of the above
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, n3 = 1. If the beam impinges at the interface between n1 and n2 with the incident angle of 60°, as shown in the figure, what is θwhen the light beam enters the layer with n3 = 1?
(A)
