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 (Mo, 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, $ = = [₁ BdA. Find the magnetic flux through the loop as a function of 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 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.) A S

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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 2.5 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 (o, T, 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, =
= [₁ BdA. Find the magnetic flux through the loop as a function of 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 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.)
A
S
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 2.5 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 (o, T, 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, = = [₁ BdA. Find the magnetic flux through the loop as a function of 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 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.) A S
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