Consider a long and thick, hollow wire with inner radius a and outer radius b. A total cur- rent I is evenly distributed across the area (i.e in the shaded region labeled 2 in the diagram). The current is running down the length of the wire so that when viewed on end it is point- ing directly into the page as indicated in the cross-section view. There is no current out- side of the wire (region 3) or in the hollow void of region 1. Side view 3 2 1+ a Cross-sectional view 1. [7pts] Use Ampere's law to calculate the magnitude B of the magnetic field B at a distance r from the center of the wire, where a < r < b. 2. [3pts] Determine the closed path integral B de along the purple triangular path shown in the schematic below. 3 N 18 Cross-sectional view 3. [10pts] Now let's assume that, perpendicular to our long and thick hollow wire with known current I, there is a conducting solenoid with an unknown current 12 running through it as shown in the figure below. We will further consider two different rectangular paths in the plane of this page (drawn in blue and red), which loop around the hollow wire in the clockwise direction. The red path also goes through 12 loops of the solenoid. (i) Express the closed path integral along the blue path, flue path B.de, in terms of known quantities and natural constants. (ii) Suppose that you have measured the total magnetic field B along the two paths and determined that fred path B·de = 5 folue path B.de Find the unknown current I2. 3 Red path 1+ Cross-sectional view Blue path (iii) If the current I2 was reversed (but still had the same magnitude as found in part ii), B de change? (YES/NO) - would the sign of fred path B de change? (YES/NO) - would the magnitude of fred path" ti 0000007
Consider a long and thick, hollow wire with inner radius a and outer radius b. A total cur- rent I is evenly distributed across the area (i.e in the shaded region labeled 2 in the diagram). The current is running down the length of the wire so that when viewed on end it is point- ing directly into the page as indicated in the cross-section view. There is no current out- side of the wire (region 3) or in the hollow void of region 1. Side view 3 2 1+ a Cross-sectional view 1. [7pts] Use Ampere's law to calculate the magnitude B of the magnetic field B at a distance r from the center of the wire, where a < r < b. 2. [3pts] Determine the closed path integral B de along the purple triangular path shown in the schematic below. 3 N 18 Cross-sectional view 3. [10pts] Now let's assume that, perpendicular to our long and thick hollow wire with known current I, there is a conducting solenoid with an unknown current 12 running through it as shown in the figure below. We will further consider two different rectangular paths in the plane of this page (drawn in blue and red), which loop around the hollow wire in the clockwise direction. The red path also goes through 12 loops of the solenoid. (i) Express the closed path integral along the blue path, flue path B.de, in terms of known quantities and natural constants. (ii) Suppose that you have measured the total magnetic field B along the two paths and determined that fred path B·de = 5 folue path B.de Find the unknown current I2. 3 Red path 1+ Cross-sectional view Blue path (iii) If the current I2 was reversed (but still had the same magnitude as found in part ii), B de change? (YES/NO) - would the sign of fred path B de change? (YES/NO) - would the magnitude of fred path" ti 0000007
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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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![Consider a long and thick, hollow wire with
inner radius a and outer radius b. A total cur-
rent I is evenly distributed across the area (i.e
in the shaded region labeled 2 in the diagram).
The current is running down the length of the
wire so that when viewed on end it is point-
ing directly into the page as indicated in the
cross-section view. There is no current out-
side of the wire (region 3) or in the hollow
void of region 1.
Side view
3
2
1+
a
Cross-sectional view
1. [7pts] Use Ampere's law to calculate the magnitude B of the magnetic field B at a distance r from the center
of the wire, where a < r < b.
2. [3pts] Determine the closed path integral B de along the purple triangular path shown in the schematic
below.
3
N
18
Cross-sectional view](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d1ae07f-bdb5-47a8-9afa-ea5a04bdf9c8%2F396d8801-8d7a-4b8c-ab2b-662c8e6571b1%2F8i1yksi_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a long and thick, hollow wire with
inner radius a and outer radius b. A total cur-
rent I is evenly distributed across the area (i.e
in the shaded region labeled 2 in the diagram).
The current is running down the length of the
wire so that when viewed on end it is point-
ing directly into the page as indicated in the
cross-section view. There is no current out-
side of the wire (region 3) or in the hollow
void of region 1.
Side view
3
2
1+
a
Cross-sectional view
1. [7pts] Use Ampere's law to calculate the magnitude B of the magnetic field B at a distance r from the center
of the wire, where a < r < b.
2. [3pts] Determine the closed path integral B de along the purple triangular path shown in the schematic
below.
3
N
18
Cross-sectional view
![3. [10pts] Now let's assume that, perpendicular to our long and thick hollow wire with known current I, there is
a conducting solenoid with an unknown current 12 running through it as shown in the figure below. We will
further consider two different rectangular paths in the plane of this page (drawn in blue and red), which loop
around the hollow wire in the clockwise direction. The red path also goes through 12 loops of the solenoid.
(i) Express the closed path integral along the
blue path, flue path B.de, in terms of known
quantities and natural constants.
(ii) Suppose that you have measured the
total magnetic field B along the two paths
and determined that
fred path
B·de = 5 folue path
B.de
Find the unknown current I2.
3
Red path
1+
Cross-sectional view
Blue path
(iii) If the current I2 was reversed (but still had the same magnitude as found in part ii),
B de change? (YES/NO)
- would the sign of fred path
B de change? (YES/NO)
- would the magnitude of fred path"
ti
0000007](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d1ae07f-bdb5-47a8-9afa-ea5a04bdf9c8%2F396d8801-8d7a-4b8c-ab2b-662c8e6571b1%2Fg90hwt_processed.png&w=3840&q=75)
Transcribed Image Text:3. [10pts] Now let's assume that, perpendicular to our long and thick hollow wire with known current I, there is
a conducting solenoid with an unknown current 12 running through it as shown in the figure below. We will
further consider two different rectangular paths in the plane of this page (drawn in blue and red), which loop
around the hollow wire in the clockwise direction. The red path also goes through 12 loops of the solenoid.
(i) Express the closed path integral along the
blue path, flue path B.de, in terms of known
quantities and natural constants.
(ii) Suppose that you have measured the
total magnetic field B along the two paths
and determined that
fred path
B·de = 5 folue path
B.de
Find the unknown current I2.
3
Red path
1+
Cross-sectional view
Blue path
(iii) If the current I2 was reversed (but still had the same magnitude as found in part ii),
B de change? (YES/NO)
- would the sign of fred path
B de change? (YES/NO)
- would the magnitude of fred path"
ti
0000007
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