課程名稱︰普通物理學甲下
課程性質︰大一必修
課程教師︰李慶德
開課學院：電資學院
開課系所︰電機工程學系
考試日期（年月日）︰2015/4/14
考試時限（分鐘）：40分鐘
試題 :
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General Physics A Quiz I April 14,2015
1 Useful Info and Formulas
→ →
◎ Gauss' law: ∮ E．dA = q/ε0, where q is the net charge enclosed in the
Gaussian surface.
-12 2 2
◎ Permittivity constant: ε0 = 8.85 x 10 C / N m
◎ Electric field and electric potential:
b → → \partial V
Vb - Va = -∫ E．ds, Es = - ────── ( partial derivative )
a \partial s
-19
◎ Elementary or fundamental charge: e = 1.602 x 10 C.
→ →
◎ Current density and drift velocity: J = n e vd, where the product ne is
carrier charge density.
l
◎ Resistance and resistivity: R = ρ── for a wire of length l and cross
A
section A.
→ → m
◎ Resistivity and current density: E = ρJ, where ρ = ─── with τand m
2
e nτ
respectively being the mean free time and the mass of electron.
◎ Electric energy stored in a capacity:
2
1 2 q
U = ─ CV = ──
2 2C
2 Do any 2 of the exam problems given below!
1. Two charges q and -q are located at (0,0,d/2) and (0,0,-d/2) on the
z-axis, respectively.
(a) Find the electric field for points on the z-axis.
(b) Find the electric field for points on the y-axis.
(c) For points on the z- and y-axis far away from the electric dipole,
check if your results for (a) and (b) are consistent with the general
formula
1 ︿ → ︿ → 3
E = ────{ 3( r．p )r - p } / r ,
4πε0
→ →
where p = qdk is the electric dipole moment and r >> d.
2. A hollow spherical conductor has an inner radius of 10 cm and an outer
radius of 20 cm. The electric field at point P just outside the outer
surface of this hollow spherical conductor has magnitude 450 N/C and is
directed outward. When an unknown charge Q is introduced into the center
of the sphere, the electric field at P is still directed outward but is
now 180 N/C.
(a) What was the net charge enclosed by the outer surface before Q was
introduced?
(b) What is charge Q?
(c) After Q is introduced, what are the charges on the inner and outer
surfaces of the conductor?
3. A plastic disk of radius a has a uniform charge density σ on one surface.
(a) Find the electric potential V(z) at any point on the central axis of
the disk, which is taken as the z-axis.
(b) From the result of (a), evaluate the electric field for points on the
central axis of the charged disk.
(c) What does the electric field become for points on the central axis
with z >> a and z << a?
4. A wire 8.00 m long and 6.00 mm in diameter has a resistance of 30.0 mΩ.
A potential difference of 24.0 V is applied between the ends.
(a) What is the current in the wire?
(b) What is the magnitude of the current density?
(c) Calculate the resistivity of the wire material.
5. A 150 kΩ resistor and a capacitor are connected in series, and a 12.0V
potential difference is suddenly applied across them. The potential
difference across the capacitor rises to 5.00 V in 1.30 μs.
(a) Calculate the time constant of the circuit.
(b) Find the capacitance of the capacitor.
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