4. (3%) What is the origin of the magnetic field? Your explanation: __(4)__

5. (5%, 本題計算過程須計分) Find an equivalent resistor Z = __(5)__ (Fig. 3 lower) for the infinite blocks of resistors (Fig. 3 upper).

6. (7%, 本題計算過程須計分) Two spherical conductors of radii r₁ and r₂ are separated by a distance much greater than the radius of either sphere. The spheres are connected by a conducting wire as shown in Fig. 4. The charges on the spheres in equilibrium are q₁ and q₂, respectively, and they are uniformly charged. Find the ratio of the magnitude of the electric field at the surface of the sphere 1 to the one of the sphere 2 is__ (6a) (3%)__. Please use the meaning of the ratio to explain the principle of a lightning rod (避雷計). Your explanation: __(6b) (4%)__

7. (5%，本題計算過程須計分) A disk of radius R has a uniform surface charge density σ (Fig. 5). Prove that magnitude of the electric field at a point P is $$E = 2\pi k_e \sigma \left[ 1 - \frac{x}{(R^2 + x^2)^{1/2}} \right]$$. Note that P lies along the central perpendicular axis of the disk and a distance x from the center of the disk. Your proof:__ (7)__

8. (2 %) What is drift speed in a conductor? Your explanation: __(8)__

9. (4 %) In normal cases, drift speed in a conductor is very slow. But, why a light bulb can be turned on immediately after switch is on? Your explanation:__ (9)__

10. (2 %) What is the back EMF? __(10)__

11. (8 %) Assume a uniformly wound solenoid having N turns and length ℓ, and ℓ is much greater than the radius of the solenoid, prove: (a) the flux through each turn of area A is ΦB = μB NIA / ℓ, and (b) the inductance is L = μ_B N² A / ℓ. Your proofs for (a): __(11a) (4%)__ and for (b)__ (11b) (4%)__

12. (4%) Please explain the Hall effect. Your explanation: __(12)__

13. (4%) Please illustrate the experiment for defining the unit for current by Ampere. Your illustration: __(13)__

14. (5 %, 本題計算過程須計分) Fig. 6 shows a very simple RL circuit with a resistor \( R \) ohms, an inductor \( L \) henries, and a battery of \( V \) volts. Prove that the current \( I(t) \) after switch is on (\( t = 0^{+} \)) is \( I(t) = (V / R)(1 - e^{-t/(L/R)}) \). Your proof:  __(14)__

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