2. Calculate the expected ratio of the magnetic field between the ends of the solenoid (x = L/2 or – L/2) and its center (x = 0) for a finite length solenoid for L~R and L » R cases by using Equation 5.4.
2. Calculate the expected ratio of the magnetic field between the ends of the solenoid (x = L/2 or – L/2) and its center (x = 0) for a finite length solenoid for L~R and L » R cases by using Equation 5.4.
Chapter16: Electromagnetic Waves
Section: Chapter Questions
Problem 2CQ: Describe the field lines of the induced magnetic field along the edge of the imaginary horizontal...
Related questions
Question
100%
![Consider the rectangular (an amperian loop) path of length L and width w shown in Figure 5.2 (right).
We can apply Ampère's law to this path by evaluating the integral of E-de over each side of the rectangle.
The contribution along side 3 is zero because the magnetic field is zero outside the solenoid. The
contributions from sides 2 and 4 are both zero, because is perpendicular to då along these paths, both
inside and outside the solenoid Side 1 gives a contribution to the integral because along this path 5 is
uniform and parallel to dž, that is, the only contribution comes from path 1.
Blds
Bids
Blds
B=0
fE dš = B đš + B-dš + B đš + B-d3 = BL = 4olenci
path 1
path 2
path 3
path 4
If N is the mumber of tums in the length L, the total curent through the rectangle is NI. Therefore,
Ampère's law applied to this path gives
N
B-ds = BL = H9NI =B = H0 = Honl
5.2
where n = N/L is the number of tums per unit length.
Consider a section of the solenoid of length dx'. The total current winding around the solenoid in that
section is dI = nidx'. This section is located at a distance x – x' away from the point P. The contribution
to the magnetic field at P due to this subset of loops is
HOR?
2[(x – x')² + R²]ª/2
HOR?
dB =
dl =-
5.3
2[(x - x')? + R2j3/2 nldx
Integrating over the entire length of the solenoid, we obtain
+L/2
|+L/2
dx'
HonIR?
(x – x')
[(x – x')² + R°j³/2
R²[(x – x')² + R*Il_1/2
Honi
x+L/2
x- L/2
5.4
2 l
(x +L/2)2 +R2
V(x- L/2)² + R²
Equation 5.4 expresses the change of magnetic field depending on the distance from the center.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc386abc3-0420-4cc0-89bb-4a7032d67409%2F08802c88-b493-466c-ab97-b7d210d3995f%2F7d5b11p_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the rectangular (an amperian loop) path of length L and width w shown in Figure 5.2 (right).
We can apply Ampère's law to this path by evaluating the integral of E-de over each side of the rectangle.
The contribution along side 3 is zero because the magnetic field is zero outside the solenoid. The
contributions from sides 2 and 4 are both zero, because is perpendicular to då along these paths, both
inside and outside the solenoid Side 1 gives a contribution to the integral because along this path 5 is
uniform and parallel to dž, that is, the only contribution comes from path 1.
Blds
Bids
Blds
B=0
fE dš = B đš + B-dš + B đš + B-d3 = BL = 4olenci
path 1
path 2
path 3
path 4
If N is the mumber of tums in the length L, the total curent through the rectangle is NI. Therefore,
Ampère's law applied to this path gives
N
B-ds = BL = H9NI =B = H0 = Honl
5.2
where n = N/L is the number of tums per unit length.
Consider a section of the solenoid of length dx'. The total current winding around the solenoid in that
section is dI = nidx'. This section is located at a distance x – x' away from the point P. The contribution
to the magnetic field at P due to this subset of loops is
HOR?
2[(x – x')² + R²]ª/2
HOR?
dB =
dl =-
5.3
2[(x - x')? + R2j3/2 nldx
Integrating over the entire length of the solenoid, we obtain
+L/2
|+L/2
dx'
HonIR?
(x – x')
[(x – x')² + R°j³/2
R²[(x – x')² + R*Il_1/2
Honi
x+L/2
x- L/2
5.4
2 l
(x +L/2)2 +R2
V(x- L/2)² + R²
Equation 5.4 expresses the change of magnetic field depending on the distance from the center.
Transcribed Image Text:2. Calculate the expected ratio of the magnetic field between the ends of the solenoid
(x = L/2 or – L/2) and its center (x = 0) for a finite length solenoid for L~R and L » R cases by
using Equation 5.4.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Classical Dynamics of Particles and Systems
Physics
ISBN:
9780534408961
Author:
Stephen T. Thornton, Jerry B. Marion
Publisher:
Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:
9780534408961
Author:
Stephen T. Thornton, Jerry B. Marion
Publisher:
Cengage Learning