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 4 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 (μo, 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, BdA. Find the magnetic flux through the loop as a function of I (I will = be proportional to I, as shown below; find the coefficient, in base SI units). Hint for (b) Φ - 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 do/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 A S (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 4 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 (μo, 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, BdA. Find the magnetic flux through the loop as a function of I (I will = be proportional to I, as shown below; find the coefficient, in base SI units). Hint for (b) Φ - 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 do/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 A S (Note: the number here will be unreasonably large. Just plug in your result.)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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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 4 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 (μo, 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,
BdA. Find the magnetic flux through the loop as a function of I (I will
=
be proportional to I, as shown below; find the coefficient, in base SI units).
Hint for (b)
Φ
-
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 do/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
A
S
(Note: the number here will be unreasonably large. Just plug in your result.)
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