Shown in the following figure is a long, straight wire and a single-turn rectangular loop, both of which lie in the plane of the page. The wire is parallel to the long sides of the loop and is 0.5 m away from the closer side. At an instant when the voltage induced in the loop is 5 V, what is the time rate of change of the current in the wire? 0.50 m 3.0 m 0.50 m a. What is the expression for magnetic field B due to the current I in the long, straight wire, at distance r away from the wire? Be . Give your answer in terms of given variables (I, r) and physical and numerical constants (140, π, ke, and/or c). Spell out Greek letters and use underscore () for subscripts. flux, $ = b. Because the magnetic field is not uniform, you will have to use integration to calculate the magnetic =[B Bd.A. Find the magnetic flux through the loop as a function of I ( will be proportional to I, as shown below; find the coefficient, i base SI units). Hint for (b) Ф I. Give your answer in terms of given variable (I); plug in numerical values of given geometric parameters and physical and numerical constants in base SI units. c. Find the rate of change of the current by setting d/dt as equal to the induced voltage and solving for dI/dt. Hint for (c) The rate of change of the current in the wire is dI dt (Note: the number here will be unreasonably large. Just plug in your result.)
Shown in the following figure is a long, straight wire and a single-turn rectangular loop, both of which lie in the plane of the page. The wire is parallel to the long sides of the loop and is 0.5 m away from the closer side. At an instant when the voltage induced in the loop is 5 V, what is the time rate of change of the current in the wire? 0.50 m 3.0 m 0.50 m a. What is the expression for magnetic field B due to the current I in the long, straight wire, at distance r away from the wire? Be . Give your answer in terms of given variables (I, r) and physical and numerical constants (140, π, ke, and/or c). Spell out Greek letters and use underscore () for subscripts. flux, $ = b. Because the magnetic field is not uniform, you will have to use integration to calculate the magnetic =[B Bd.A. Find the magnetic flux through the loop as a function of I ( will be proportional to I, as shown below; find the coefficient, i base SI units). Hint for (b) Ф I. Give your answer in terms of given variable (I); plug in numerical values of given geometric parameters and physical and numerical constants in base SI units. c. Find the rate of change of the current by setting d/dt as equal to the induced voltage and solving for dI/dt. Hint for (c) The rate of change of the current in the wire is dI dt (Note: the number here will be unreasonably large. Just plug in your result.)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter31: Faraday’s Law
Section: Chapter Questions
Problem 31.48P: A motor in normal operation carries a direct current of 0.850 A when connected to a 120-V power...
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Transcribed Image Text:Shown in the following figure is a long, straight wire and a single-turn rectangular loop, both of which lie in
the plane of the page. The wire is parallel to the long sides of the loop and is 0.5 m away from the closer
side. At an instant when the voltage induced in the loop is 5 V, what is the time rate of change of the
current in the wire?
0.50 m
3.0 m
0.50 m
a. What is the expression for magnetic field B due to the current I in the long, straight wire, at
distance r away from the wire?
B=
Give your answer in terms of given variables (I, r) and
physical and numerical constants (40, π, ke, and/or c). Spell out Greek letters and use underscore
() for subscripts.
b. Because the magnetic field is not uniform, you will have to use integration to calculate the magnetic
flux, =
proportional to I, as shown below; find the coefficient, i base SI units).
S Bd.A. Find the magnetic flux through the loop as a function of I ( will be
Hint for (b)
6=
I. Give your answer in terms of given variable (I); plug in numerical
values of given geometric parameters and physical and numerical constants in base SI units.
c. Find the rate of change of the current by setting d/dt as equal to the induced voltage and solving
for dI/dt.
Hint for (c)
Submit Question
dI
The rate of change of the current in the wire is dt
(Note: the number here will be unreasonably large. Just plug in your result.)
A
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