课程名称︰电磁学上 课程性质︰物理系双班必带 课程教师︰王立民 开课学院：理学院 开课系所︰物理系 考试日期（年月日）︰99/12/16 考试时限（分钟）：120分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 考试范围：CH3.2.2~CH4.3 1. Find the potential inside and outside a spherical shell that carries a uniform surface charge σ0. (10%) 2. Using general solution with cylindrical symmetry: ∞ V(s,ψ)=a0+b0lns+Σ[s^k(akcoskψ+bksinkψ)+s^-k(ckcoskψ+dksinkψ)] k=1 Find (a) the potential outside an infinitely long metel pipe, of radius R, placed at right angles to an otherwise uniform electric field E0, and (b) the surface charge induced on the pipe.(20%) 3. (a) Using the method of images, determine the electric field outside a spherical conducting shell (radius R) placed in a uniform electric field E0. [Hint: the same image charges as those for a conducting sphere, and using 1/r+ - 1/r- ≒ d/(r^2 cosθ), where d is the separated distance between r+ and r-.](10%) (b) Find the induced surface charge density.(5%) (c) Calculate the dipole moment due yo the induced surface charge.(5%) ^ 4. A sphere of radius R carries a polarization P(r)= kr^2 r, where k is a ^ constant and r r is the vector from the center. (a) Calculate the bound charge σb and ρb.(10%) (b) Find the field inside and outside the sphere.(10%) (c) Find the electric displacement inside and outside the sphere.(10%) 5. The electron cloud for a hydrogen atom in the ground state has a charge density: ρ(r)=(q/πa^3)*e^(-2r/a), where q is the charge of the electron and a is the Bohr radius. (a) Find the atomic polarizability of this atom.(10%) (b) A point charge Q is situated a large distance r(r>>a) from the neutral hydrogen atom. Find the force of attraction between them.(10%) Hint: using these formulas: r ∫[e^(-2r/a)*r^2]dr=-0.5a[e^(-2r/a)*(r^2-ar+0.5a^2)-0.5a^2] 0 e^x = 1 + x + x^2/2! + x^3/3! +..... ^ ︿ The field due to a dipole: E(r,θ)=p/(4πε0r^3)*(2cosθ r+sinθ θ) 6. A very long cylinder, of radius a, carries a uniform (not "radial") polarization P perpendicular to its axis, and there is no free charge on it. (a) Find the electric field inside and outside the cylinder.(10%) (b) Find the electric displacement inside and outside the cylinder. Is it zero? And explain your answer.(10%) Hint: using the approximation: (s and d are vectors.) s-d/2 1 (s．d) d ──── ≒──(s+s───-─) (s-d/2)^2 s^2 s^2 2 s+d/2 1 (s．d) d ─────≒──(s-s───+─), for |s|>>|d| (s+d/2)^2 s^2 s^2 2 --

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