課程名稱︰普通物理學甲下
課程性質︰物理系必帶
課程教師︰邱雅萍
開課學院：理學院
開課系所︰物理學系
考試日期（年月日）︰2019年4月23日
考試時限（分鐘）：180分鐘
是否需發放獎勵金：是
(如未明確表示，則不予發放）
試題 :
General Physics-Midterm Exam
Date:2019/4/23 (Tue.) 10:20
1.[10%] Write down the Maxwell's equations and explain the physical meaning
for each of them.
2.[15%] The point P is located above the center of a flat circular disk of ra-
dius R along the z axis by a distance z (Fig 1). The circular disk carriers
a uniform surface charge σ. (a)Find the electric field of the point P. (b)
Find the electric potential of the point P. (c)What does your result of (a)
and (b) when the condition is in the limit z>>R?
3.[10%] In Fig.2, p1 and p2 are (perfect) dipoles a distance r apart initially
. If the dipoles are freely to rotate. What is the stable case of the dipole
alignment in the following selection?
(a)↑↓;(b)↑↑;(c)↑→;(d)→←;(e)←→. [You may have to answer the questi-
on by explanation, instead of only selecting the answer.]
4.[30%] A circular loop of radius R carries a steady current I.(Fig.3)
(a)(5%) What is the magnetic dipole moment of the circular loop in Fig.3?
(b)(5%) Find the magnetic field a distance z above the center of a circular
loop (see Fig.3).
(c)(5%)Use the result of (b) and find the magnetic field at point P on the
axis of a tightly wound solenoid in Fig.4. The solenoid consists of n tu-
rns per unit length wrapped around a cylindrical tube of a radius a and
carrying current I (Fig.4). Express your answer in terms of θ1 and θ2.
(d)(5%)Continue the results in (c). What is the field on the axis of an
infinite solenoid?
(e)(10%)The total resistance of the solenoid is 0.1 ohm. Derive the equation
describing the current as a function of time immediately after connecting
the solenoid to a 20 Volt power supply. In addition, what is the time
constant of the circuit?
5.[15%] The electric field of an electromagnetic wave in vacuum is given by
Ex=0,
Ey=30cos(2π×10^8t-2πx/3),
Ez=0,
where E is in Volt/meter, t in seconds, and x in meters.
Determine: (a)the frequency f and the wavelength λ; (b)the direction of pr-
opagation of the wave; (c)the direction of the magnetic field.
6.[20%] A parallel plate capacitor (having perfectly conducting plate) with
plate seperation d is filled with two layers of material (1) and (2). The
first layer has dielectric constant ε1, conductivity σ1, the second, ε2,
σ2, and their thicknesses are d1 and d2, respectly. A potential V is placed
across the capacitor (see Fig.5). Neglect edge effects.
(a) What is the electric field in material (1) and (2)?
(b) What is the current density flowing through the capacitor?
(c) What is the total surface charge density on the interface between (1)
and (2).
(d) What is the free surface charge density on the interface between (1) and
(2)?
[Hint: the definition of the current density is J=σE]
[Hint: Boundary condition: n‧(E2-E1)=σt/ε0, σt means the total surface
charge density.]
7.[10%] In Fig.6, initially, the switch S is opened for a long time. At time
t=0, S is closed. Calculate the current IL through the inductor as a functi-
of the time.
8.[10%] In Fig.7 two conductors of infinite length carry a current I. They are
parallel and seperated by a distance 2a. A circular conducting ring of radi-
us a in the plane of the parallel wires lies between the two straight condu-
ctors and is insulated from them. Find the coefficient of mutual inductance
between the circular conductor and the two straight conductors.
Fig.1：https://imgur.com/t3x1zE3
Fig.2
Fig.3：https://imgur.com/x2jRIFX
Fig.4
Fig.5：https://imgur.com/q7MoAUt
Fig.6
Fig.7：https://imgur.com/mBUaDRu