課程名稱: 普通物理一A 課程性質: 課程教師: 余怡德 開課系所: 物理系 考試時間: 95.5.11 試題 : 1.A current i is flowing in a flat conducting strip,of width w and thickness t The current carriers with +q are forced to move with a drift speed v_d.If the conducting strip id put in a magnetic field B with direction shown in figure, the Hall potential difference is V_H = __________.The number density of the current carriers n = _____________.(8%) figure: t ___ ╲ ╲ B ｜ ╲ ╲ ↗ ｜ ╲ ╲ w ∣ ╲ ╲ ∣ ↘ ╲_╲ ∣ v_d ｜ ｜ ╲ ｜ ｜ ╲ ｜ ｜ ╲ ｜ ︱ ╲｜ ｜ ↘ i ￣￣ 2. A box with two terminals is known to contain a few electric elements which are connected in series.If an AC signal with V_rms = 1.0(V) is input to the box from terminals.the rms value of the AC current I_rms reaches a maximum value of 0.08(A) when the frequency of the input signal is 1000 (cycles/sec). If the frequency is changed to 1050 (cycles/sec) with V_rms unchanged,then I_rms = 0.04 (A).Please write down the components in the circuit abd their values.(12%) 元件: __________,__________,__________ 數值: __________,__________,__________ 3.A rectangular loop of dimensions h and d is placed a distance R from a infinitely long straight wire carrying a current I = i_0cos(ωt).The loop and the wire are in the same plane,and the two side of length h are parallel to the wire.Please find (a) the expression ____________ of the induced emf around the loop,and (b) the direction of the emf when 0 < ωt <2π.(8%) figure: | | _______ I | | | ↑ | | | | | | | |_______| | ←→ ← d → | R 4.In the circuit shown in the figure on the right ,ε= 10(V),R_1 = 3.0 (Ω) R_2 = 6.0 (Ω),and L = 5.0 (H).For (a) switvch s is just close,find the current i_1 thrugh R_1,i_1 = _______.(b) switch is closed for a long time,find the current i_2 through R_2, i_2 = ________.(8%) figure: s ______╱ ______╴╴╴╴╴ ｜ ｜ ｜ ｜ ︴ ︴ L ε ￣￣ R_1 ︴ ｜ ┬ ︴ ︴R_2 ｜ ｜ ｜ ｜ ｜ ｜ ￣￣￣￣￣￣￣￣￣￣￣￣￣ 5.The system,shown in the figure,is to transform the electrical energy to the mechanical energy.Two long parallel guide wires,of zero resistance,separated by a distance l,are conected to a potential difference ε.A bar of resistance R makes contact with these wires,and can slide parallel to itsself ( always perpendicular to the wires ).Ab externally applied uniform magnetic field B is perpendicular to the plane of the bar and the wires. (a)If there is no external mechanical load,what is the steady-state speed of reached by the bar. (b)If the mass of the bar is m,obtain the equation of motion of the speed of the bar. (c)Solve the equation of motion and obtain the speed of the bar as a function of time t,assuming the bar starts from rest at t=0.(18%) figure: bar ｜￣￣￣￣∥￣￣￣￣￣￣￣￣｜ ∣ ∥ ｜ ε ￣￣ ∥ ∣ ￣ ∥ ∣ 磁場 B 進入紙面 ｜ ∥ ∣ ｜ ∥ ∣ ｜ ∥ ∣ ￣￣￣￣￣ ￣￣￣￣￣￣￣￣ 6.A plastic disk of radius R has charge Q distributed uniformly over its surface.The disk rotates at a frequency f about its axis.Please calculate (a)the dipole moment μ of th disk,and (b)the magnetic field B at the center of the disk.(16%) 7.The current density J inside a long ,solid,cylindrical wire of radius 3.1(mm) is in the direction of the centeral axis,and its magnetic varies linearly with radial distance r from the axis according to J=(J_0)r/a ,where J_0 = 310(A/m^2) and a = 3.1(mm).Find the magnitude of the magnetic field at (a) r = 0 (b) r = a/2 ,(c) r = 2a. (15%) 8.Write down the Maxwell's equations and names of the related physical laws for the electromagnetic field.(16%) (a)______________________________________. (b)______________________________________. (c)______________________________________. (d)______________________________________. --

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