复旦大学物理学系 2006~2007学年第二学期期末考试试卷 卷 课程名称:大学物理(下)课程代码:PHYS120002.05 开课院系:物理学系 考试形式:闭卷 姓名 学号 专业 题号 总分 得分 Electric constant 6o=8.85x10-12C2/(N.m2) Magnetic constant u0=4z×10N/A2=1.26×10°H/m Plank constant h=663x10-34.s=4.14x10er s Neutron mass 1675×10-kg 1. Derive an expression for the work required by an external agent to put the four charges together as indicated in the figure below. Each side of the square has
2. In the laboratory we produce magnetic fields using current-carrying wires rather than the motion of individual charges. To describe the magnetic field due to a current, we have the biot-Sanvart law B=s Consider the circuit of the figure below. The curved segments are arcs of circles of radii a and b: The straight segments are along the radii. find the magnetic field at P, assuming a current i in the circuit. (15%)
3.(a)We can write the electric and magnetic fields in the usual mathematical form of a sinusoidal traveling wave E(x, )=Em sin(kx-ar), B(x, s)=Bm sin(kx-aor) From Faraday's law, we have B Find the ratio of the amplitudes of the electric to the magnetic components of the
wave.(b)A vector called the Poynting vector is defined by s=E×B Please explain what this vector means. Note that it is a vector. (c)A radio station radiates a sinusoidal wave with an average total power of 50 kw. Assuming it radiates equally in all directions (which is unlikely in real-world situations), find the amplitudes of the electric and the magnetic components of the wave at a distance of 100 km from the antenna. (2%+4%+9%)
4.(a) Find the speed and the kinetic energy of a neutron having a de broglie wavelength of 0. 1 nm, typical of atomic spacing in crystals. (b) Label as true or false these statements involving the quantum numbers n, l, my. If a statement is false, write the correct one (1)The values of m that are allowed depend only on l and not on n(2) The n=4 shell contains four subshells. 3) The smallest value of n that can go with a i gIven Z is 1+1.(4)All states with H0 also have mo, regardless of the value of n (5) Every shell contains n subshells.(6)One of these subshells cannot exist: n=2, 1-1 n4, 1-3; n=3, 1-2; n=l, l-l.(c)For a hydrogen atom with F-l, the measured value of L, is 0. Find the possible values Lx can have.(6%+2%x6+2%) 5. Consider a grating with N slits, where the slit width a is assumed to be much smaller than the light wavelength. (a)Derive the intensity expression for the diffracted lights on the screen that is assumed far way from the grating. (b)Find the positions of the principal maxima of the diffraction pattern. (15%+5%)