College Physics:
11th Edition
ISBN: 9781305965515
Author: SERWAY, Raymond A.
Publisher: Brooks/Cole Pub Co
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Chapter 16, Problem 25P
Calculate the speed of (a) an electron and (b) a proton with a kinetic energy of 1.00 electron volt (eV). (c) Calculate the average translational kinetic energy in cV of a 3.00 × 102 K ideal gas particle. (Recall from Topic 10 that
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An electron is fired at a speed vo = 5.6 x 10° m/s and at
an angle 6, = -45° between two parallel conducting plates
that are D = 2.0 mm apart, as in Figure P16.72. If the volt-
age difference between the plates is AV = 100. V, determine
(a) how close, d, the electron will get to the bottom plate and
(b) where the electron will strike the top plate.
+ + + + + + + +
Path of
the electron
AV
Figure P16.72
Two concentric spherical conducting shells are separated by vacuum. The inner shell has total charge +Q
and radius a, and outer shell has charge -Q and radius b. Using integration of the electric field energy
density find the electric energy stored in the system. Take Q = 28 µC, a = 20 cm and b = 70 cm.
I
1
The energy, U₁ = 12.582440✔✔ Units J
The energy, U₁
a
=
=
Using the obtained energy and formula for the energy stored in a capacitor, U
capacitance of the system.
The capacitance, Co 3.1154528 X Units Select an answer ✓
Repeat the calculations for the same system with a dielectric material of k = 4.5 inserted in between the
shells.
The capacitance, C₁
=
-Q
Units Select an answer ✓
.37489732 X Units pF
Q²
20¹
find the
Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function:
E = αe-r/a0 + β/r + b0
where alpha (α), beta (β), a0 and b0 are constants. Find an expression for its capacitance.
First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by:
Calculating the antiderivative or indefinite integral ,
Vab = (-αa0e-r/a0 + β + b0 )
By definition, the capacitance C is related to the charge and potential difference by:
C = /
Evaluating with the upper and lower limits of integration for Vab, then simplifying:
C = Q / ( (e-rb/a0 - e-ra/a0) + β ln() + b0 () )
Chapter 16 Solutions
College Physics:
Ch. 16.1 - If an electron is released from rest in a uniform...Ch. 16.1 - If a negatively charged particle is placed at rest...Ch. 16.1 - Figure 16.3 is a graph of an electric potential as...Ch. 16.1 - If a negatively charged particle is placed at...Ch. 16.2 - Consider a collection of charges in a given region...Ch. 16.2 - A spherical balloon contains a positively charged...Ch. 16.3 - An electron initially at rest accelerates through...Ch. 16.6 - A capacitor is designed so that one plate is large...Ch. 16.7 - A parallel-plate capacitor is disconnected from a...Ch. 16.8 - A fully charged parallel-plate capacitor remains...
Ch. 16.8 - Consider a parallel-plate capacitor with a...Ch. 16 - A proton is released from rest in a uniform...Ch. 16 - An electron is released from rest in a uniform...Ch. 16 - Figure CQ16.3 shows equipotential contours in the...Ch. 16 - Rank the potential energies of the four systems of...Ch. 16 - A parallel-plate capacitor with capacitance C0...Ch. 16 - An air-filled parallel-plate capacitor with...Ch. 16 - Choose the words that make each statement correct,...Ch. 16 - Why is it important to avoid sharp edges or points...Ch. 16 - Explain why, under static conditions, all points...Ch. 16 - If you are given three different capacitors C1,...Ch. 16 - (a) Why is it dangerous to touch the terminals of...Ch. 16 - The plates of a capacitor are connected to a...Ch. 16 - Rank the electric potentials at the four points...Ch. 16 - If you were asked to design a capacitor in which...Ch. 16 - Is it always possible to reduce a combination of...Ch. 16 - Explain why a dielectric increases the maximum...Ch. 16 - A uniform electric field of magnitude 375 N/C...Ch. 16 - A proton is released from rest in a uniform...Ch. 16 - A potential difference of 90.0 mV exists between...Ch. 16 - Cathode ray tubes (CRTs) used in old-style...Ch. 16 - A constant electric field accelerates a proton...Ch. 16 - A point charge q = +40.0 C moves from A to B...Ch. 16 - Oppositely charged parallel plates are separated...Ch. 16 - (a) Find the potential difference VB required to...Ch. 16 - An ionized oxygen molecule (O+2) at point A has...Ch. 16 - On planet Tehar, the free-fall acceleration is the...Ch. 16 - An electron is at the origin, (a) Calculate the...Ch. 16 - The two charges in Figure P16.12 are separated by...Ch. 16 - (a) Find the electric potential, taking zero at...Ch. 16 - Three charges are situated at corners of a...Ch. 16 - Two point charges Q1 = +5.00 nC and Q2 = 3.00 nC...Ch. 16 - Three identical point charges each of charge q are...Ch. 16 - The three charges in Figure P16.17 are at the...Ch. 16 - A positive point charge q = +2.50 nC is located at...Ch. 16 - A proton is located at the origin, and a second...Ch. 16 - A proton and an alpha particle (charge = 2e, mass...Ch. 16 - A tiny sphere of mass 8.00 g and charge 2.80 nC is...Ch. 16 - The metal sphere of a small Van de Graaff...Ch. 16 - In Rutherfords famous scattering experiments that...Ch. 16 - Four point charges each haring charge Q are...Ch. 16 - Calculate the speed of (a) an electron and (b) a...Ch. 16 - An electric field does 1.50 103 eV of work on a...Ch. 16 - An alpha particle, which has charge 3.20 1019 C,...Ch. 16 - In the classical model of a hydrogen atom, an...Ch. 16 - Consider the Earth and a cloud layer 8.0 102 m...Ch. 16 - (a) When a 9.00-V battery is connected to the...Ch. 16 - An air-filled parallel-plate capacitor has plates...Ch. 16 - Air breaks down and conducts charge as a spark if...Ch. 16 - An air-filled capacitor consists of two parallel...Ch. 16 - A 1-megabit computer memory chip contains many...Ch. 16 - a parallel-plate capacitor with area 0.200 m2 and...Ch. 16 - A small object with a mass of 350. g carries a...Ch. 16 - Given a 2.50-F capacitor, a 6.25-F capacitor, and...Ch. 16 - Two capacitors, C1 = 5.00 F and C2 = 12.0 F, are...Ch. 16 - Find (a) the equivalent capacitance of the...Ch. 16 - Two capacitors give an equivalent capacitance of...Ch. 16 - For the system of capacitors shown in Figure...Ch. 16 - Consider the combination of capacitors in Figure...Ch. 16 - Find the charge on each of the capacitors in...Ch. 16 - Three capacitors are connected to a battery as...Ch. 16 - A 25.0-F capacitor and a 40.0-F capacitor are...Ch. 16 - (a) Find the equivalent capacitance between points...Ch. 16 - A 1.00-F capacitor is charged by being connected...Ch. 16 - Four capacitors are connected as shown in Figure...Ch. 16 - A 12.0 V battery is connected to a 4.50 F...Ch. 16 - Two capacitors, C1 = 18.0 F and C2 = 36.0 F, are...Ch. 16 - A parallel-plate capacitor has capacitance 3.00 F....Ch. 16 - Each plate of a 5.00 F capacitor stores 60.0 C of...Ch. 16 - The voltage across an air-filled parallel-plate...Ch. 16 - (a) How much charge can be placed on a capacitor...Ch. 16 - Determine (a) the capacitance and (b) the maximum...Ch. 16 - A parallel-plate capacitor has plates of area A =...Ch. 16 - A model of a red blood cell portrays the cell as a...Ch. 16 - When a potential difference of 150. V is applied...Ch. 16 - Three parallel-plate capacitors are constructed,...Ch. 16 - For the system of four capacitors shown in Figure...Ch. 16 - A parallel-plate capacitor with a plate separation...Ch. 16 - Two capacitors give an equivalent capacitance of...Ch. 16 - A parallel-plate capacitor is constructed using a...Ch. 16 - Two charges of 1.0 C and 2.0 C are 0.50 m apart at...Ch. 16 - Find the equivalent capacitance of the group of...Ch. 16 - A spherical capacitor consists of a spherical...Ch. 16 - The immediate cause of many deaths is ventricular...Ch. 16 - When a certain air-filled parallel-plate capacitor...Ch. 16 - Capacitors C1 = 6.0 F and C2 = 2.0 F are charged...Ch. 16 - Two positive charges each of charge q are fixed on...Ch. 16 - Metal sphere A of radius 12.0 cm carries 6.00 C of...Ch. 16 - An electron is fired at a speed v0 = 5.6 106 m/s...
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