6. (10%) Two infinitely long, parallel wires are lying on the ground a distance a meter apart as shown in Figure 6. A third wire, of length L meter and mass m kg, carries a current of I₁ Ampere and is levitated above the first two wires, at a horizontal position midway between them. The infinitely long wires carry equal currents I₂ in the same direction, but in the direction opposite that in the levitated wire. What current must the infinitely long wires carry so that the three wires form an equilateral triangle?



Figure 7

7. (10%) In an experiment designed to measure the magnitude of a uniform magnetic field, electrons are accelerated from rest through a potential difference of ΔV Voltage and then enter a uniform magnetic field that is perpendicular to the velocity vector of the electrons. The electrons travel along a curved path because of the magnetic field of B Tesla (Such a curved beam of electrons is shown in Figure 7). What is the radius of the curved beam as shown in Figure 7? Note that the mass of an electron is mₑ kg and an electron contains e Coulomb charges.

8. (10%) Suppose two infinite planes of charge are parallel to each other (Figure 8), one positively charged and the other negatively charged. The positively and negatively charged planes have charge densities of $\sigmap$ and $-\sigman$, respectively. What is the directions and magnitudes of electric field at point P1 (to the left of the positively charged plane)?Figure 8

9. (10%) The electric potential at the position of a point \( P \) in three dimensions be given by the vector \( r = (x, y, z) \) in Cartesian Coordinates is \( (x^2 + y^2 + z^2)^{-0.5} \). Please find the magnitude of the electric field at the point \( (1, 1, 1) \).

10. (10%) Assume a uniformly wound solenoid having \( N \) turns and length \( \ell \), and \( \ell \) is much greater than the radius of the solenoid, find the inductance of this solenoid. Assume \( \mu_0 \) is the permeability of vacuum.

1. A particle with charge \( Q \) is located a small distance \( \delta \) immediately above the center of the flat face of a hemisphere of radius \( R \) as shown in Fig. 1. What is the electric flux (a) through the curved surface and (b) through the flat face as \( \delta \rightarrow 0 \)? (5 points for each)

2. Four balls, each with mass \( m \), are connected by four nonconducting strings to form a square with side \( a \) as shown in Fig. 2. The assembly is placed on a nonconducting, friction-less, horizontal surface. Balls 1 and 2 each have charge \( q \), and balls 3 and 4 are uncharged. After the string connecting balls 1 and 2 is cut, what is the maximum speed of balls 1 and 2? (10 points)

3. Two large, parallel metal plates, each of area \( A \), are oriented horizontally and separated by a distance \( 3d \). A grounded conducting wire joins them, and initially each plate carries no charge. Now a third identical plate carrying charge \( Q \) is inserted between the two plates, parallel to them and located a distance \( d \) from the upper plate as shown in Fig. 3. Find: (a) What induced charge appears on each of the two original plates? (4 points) (b) What potential difference appears between the middle plate and each of the other plates? (3 points) (c) What is the capacitance? (3 points)

4. The circuit in Fig. 4 has been connected for several seconds. Find the current (a) in the \( 4.00\mathrm{-V} \) battery, (b) in the \( 3.00\mathrm{-}\Omega \) resistor, (c) in the \( 8.00\mathrm{-V} \) battery, and (d) in the \( 3.00\mathrm{-V} \) battery. (e) Find the charge on the capacitor (2 points for each). (以科學記號表示且四捨五入至小數點3位)

5. Please briefly explain (a) Faraday's Law of Induction (5 points), and (b) Lenz's Law (5 points).

6. Explain (a) the origin of the magnetic field and (b) what the Eddy Currents is (5 points for each).

109年 - 109 國立臺北大學_學士班曁進修學士班轉學生招生考試試題_通訊工程學系日間學士班2年級：物理學#147379

108年 - 108 國立臺北大學_日間學士班轉學生招生考試試題_通訊工程學系日間學士班2年級：物理學#147376

107年 - 107 台灣聯合大學系統_學士班轉學考試_A3/A6/A7：普通物理#99865

106年 - 106 國立臺北大學_學士班曁進修學士班轉學生招生考試試題_通訊工程學系2年級：物理學#147375

106年 - 台聯大轉學考 普通物理#99773

105年 - 105 國立臺北大學_日間學士班曁進修學士班轉學生招生考試試題_通訊工程學系日間學士班2年級：物理學#147377

105年 - 105 台灣聯合大學系統_學士班轉學生考試試題：普通物理#124919

105年 - 105年地方四等-普通物理學概要#58765

105年 - 105年地方三等-近代物理#58638

105年 - 105年高等三級暨普通考高考三級原子物理  #57777