Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
4th Edition
ISBN: 9780134110684
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Chapter 27, Problem 65EAP
A wire of radius R has a current density that increases linearly with distance from the center of the wire:
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A wire has a radius of 2.5 m. The current density carried by the wire is a function of distance from the center of the wire is given by J(r) = C exp(-r2/L2) (A/m2), where C = 7.6 A/m2, and L = 2.7 m. Calculate the total amount of current carried by the wire, in A.
(Please answer to the fourth decimal place - i.e 14.3225)
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The diameter of the copper wire is h=1.3 mm . It carries 2.68 A constant current. There are 8.5×1028 free electrons in copper per cubic meter.
What is the cross-sectional area of the wire (μm2 )?
Chapter 27 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 27 - Prob. 1CQCh. 27 - Prob. 2CQCh. 27 - The electron drift speed in a wire is exceedingly...Ch. 27 - Prob. 4CQCh. 27 - Prob. 5CQCh. 27 - All the wires in FIGURE Q27.6 are made of the same...Ch. 27 - Both batteries in FIGURE Q27.7 are ideal and...Ch. 27 - Both batteries in FIGURE Q27.8 are ideal and...Ch. 27 - The wire in FIGURE Q27.9 consists of two segments...Ch. 27 - Prob. 10CQ
Ch. 27 - ll. The wires in FIGURE Q27.11 are all made of the...Ch. 27 - Which, if any, of these statements are true? (More...Ch. 27 - Prob. 1EAPCh. 27 - Prob. 2EAPCh. 27 - .0 × 1016 electrons flow through a cross section...Ch. 27 - Prob. 4EAPCh. 27 - Prob. 5EAPCh. 27 - Prob. 6EAPCh. 27 - Prob. 7EAPCh. 27 - Prob. 8EAPCh. 27 - Prob. 9EAPCh. 27 - Prob. 10EAPCh. 27 - Prob. 11EAPCh. 27 - The current in an electric hair dryer is 10.0 A....Ch. 27 -
13. When a nerve cell fires, charge is...Ch. 27 - Prob. 14EAPCh. 27 - Prob. 15EAPCh. 27 - Prob. 16EAPCh. 27 - Prob. 17EAPCh. 27 - Prob. 18EAPCh. 27 - Prob. 19EAPCh. 27 - Prob. 20EAPCh. 27 - Prob. 21EAPCh. 27 - Prob. 22EAPCh. 27 - Prob. 23EAPCh. 27 - 24. The two segments of the wire in FIGURE EX27.24...Ch. 27 - A 1.5 V battery provides 0.50 A of current. a. At...Ch. 27 - Prob. 26EAPCh. 27 - Prob. 27EAPCh. 27 - Prob. 28EAPCh. 27 - Prob. 29EAPCh. 27 - Prob. 30EAPCh. 27 - Prob. 31EAPCh. 27 - Prob. 32EAPCh. 27 - Prob. 33EAPCh. 27 - Prob. 34EAPCh. 27 - Prob. 35EAPCh. 27 - Prob. 36EAPCh. 27 - Prob. 37EAPCh. 27 - Prob. 38EAPCh. 27 - Prob. 39EAPCh. 27 - Prob. 40EAPCh. 27 - Prob. 41EAPCh. 27 - Prob. 42EAPCh. 27 - Prob. 43EAPCh. 27 - Prob. 44EAPCh. 27 - Prob. 45EAPCh. 27 - Prob. 46EAPCh. 27 - Prob. 47EAPCh. 27 - Prob. 48EAPCh. 27 - Prob. 49EAPCh. 27 - Variations in the resistivity of blood can give...Ch. 27 - The conducting path between the right hand and the...Ch. 27 - The conductive tissues of the upper leg can be...Ch. 27 - The resistivity of a metal increases slightly with...Ch. 27 - Prob. 54EAPCh. 27 - You need to design a 1.0 A fuse that “blows” if...Ch. 27 - I A hollow metal cylinder has inner radius a....Ch. 27 - A hollow metal sphere has inner radius a, outer...Ch. 27 - The total amount of charge in coulombs that has...Ch. 27 - The total amount of charge that has entered a wire...Ch. 27 - The current in a wire at time t is given by the...Ch. 27 - The current supplied by a battery slowly decreases...Ch. 27 - The two wires in FIGURE P27.62 are made of the...Ch. 27 - What diameter should the nichrome wire in FIGURE...Ch. 27 - An aluminum wire consists of the three segments...Ch. 27 - A wire of radius R has a current density that...Ch. 27 - A 0.60 -mm-diameter wire made from an alloy (a...Ch. 27 - A 20 -cm-long hollow nichrome tube of inner...Ch. 27 - Prob. 68EAPCh. 27 - Prob. 69EAPCh. 27 - Prob. 70EAPCh. 27 - Prob. 71EAPCh. 27 - Prob. 72EAPCh. 27 - Prob. 73EAPCh. 27 - Prob. 74EAPCh. 27 - Prob. 75EAPCh. 27 - Prob. 76EAP
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- What is the current in a wire of radius R = 2.08 mm if the magnitude of the current density is given by (a) Ja = Jor/R and (b) Jp = Jo(1 - r/R) in which r is the radial distance and Jo = 8.05 × 104 A/m2? (c) Which function maximizes the current density near the wire's surface? (a) Number i Units (b) Number i Units (c)arrow_forwardHelparrow_forwardA current of I = 1.1 A is passing through a conductor with cross sectional area A = 3.5 × 10-4 m2. The charge carriers in the conductor, electrons, have a number density n = 7.7 x 1027 m-3. Part (a) Express the drift velocity of electrons through I, A, n, and the fundamental charge e. vd = (I/A n e) is an incorrect equation. Part (b) Calculate the numerical value of v, in m/s. vd =arrow_forward
- A current of I = 7.62 A is passing through a conductor with cross sectional area A = 7.11 × 104 m². The charge carriers in the conductor, electrons, have a number density of n = 6.39 x 1027 m-3. Enter an expression for the drift velocity of electrons in terms of the current, I, the cross-sectional area, A, the number density, n, and the fundamental charge, e. What is the numerical value, in meters per second, of the drift velocity?arrow_forwardA current of I = 4.6 A is passing through a conductor with cross sectional area A = 3.5 × 10-4 m2. The charge carriers in the conductor, electrons, have a number density n = 1.2 x 1027 m-3. Part (a) Express the drift velocity of electrons through I, A, n, and the fundamental charge e. Part (b) Calculate the numerical value of v, in m/s.arrow_forwardA current of I = 7.3 A is passing through a conductor with cross sectional area A = 6.5 × 10-4 m2. The charge carriers in the conductor, electrons, have a number density n = 2.1 x 1027 m-3. Calculate the numerical value of the drift velocity, v, in m/s. vd =arrow_forward
- What is the current in a wire of radius R = 3.08 mm if the magnitude of the current density is given by (a) Ja = Jor/R and (b) J = Jo(1-r/R) in which r is the radial distance and Jo = 3.50 x 104 A/m²? (c) Which function maximizes the current density near the wire's surface? (a) Number i (b) Number i Units Unitsarrow_forwardA long silver metal rod with a circular cross-section has an estimated diameter of cross-section 1 mm. You set up the rod so that a current of 2 A flows through the cross-section. Also, 5.0x1028 m-3 is the free electron density of silver. What is the magnitude of the drift speed of the electron flowing in the rod?arrow_forwardWhat is the current in a wire of radius R = 4.48 mm if the magnitude of the current density is given by (a) Ja = J0r/R and (b) Jb = J0(1 - r/R) in which r is the radial distance and J0 = 7.93 × 104 A/m2? (c) Which function maximizes the currentdensity near the wire’s surface?arrow_forward
- A copper wire has a circular cross section with a radius of 1.81 mm. HINT Apply the relation between electrical current and drift speed. Click the hint button again to remove this hint. (a) If the wire carries a current of 3.68 A, find the drift speed (in m/s) of electrons in the wire. (Take the density of mobile charge carriers in copper to be n = 1.10 x 1029 electrons/m³.) m/s (b) For the same wire size and current, find the drift speed (in m/s) of electrons if the wire is made of aluminum with n = 2.11 x 102⁹ electrons/m³. m/sarrow_forwardThe magnitude Jof the current density in a certain wire with a circular cross section of radius R = 2.28 mm is given by J = (3.18 × 10®)r2, with J in amperes per square meter and radial distance r in meters. What is the current through the outer section bounded by r = 0.927R andr = R? Number Unitsarrow_forwardYou find a long silver metal rod with a circular cross-section and you measure its cross-section diameter to be 1 mm. You set the rod up in a way that a current of 2 A passes through its cross-section. The free- electron density of silver is 5.9 × 1028 m-3. Given this information, what is the magnitude of the drift speed of the electrons flowing in the rod? (Express the speed in mm/s with two decimal places)arrow_forward
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