(a) Determine the magnetic flux density inside of a very long solenoid (b, n2, 1) using Ampere's law. (b) Now assume that a short solenoid (a, n₁, 1) lies inside of this long solenoid. Calculate the mutual inductance of these two solenoids.
(a) Determine the magnetic flux density inside of a very long solenoid (b, n2, 1) using Ampere's law. (b) Now assume that a short solenoid (a, n₁, 1) lies inside of this long solenoid. Calculate the mutual inductance of these two solenoids.
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(a) Determine the magnetic flux density inside of a very long solenoid (b, n₂, 1) using
Ampere's law.
(b) Now assume that a short solenoid (a, n, l) lies inside of this long solenoid.
Calculate the mutual inductance of these two solenoids.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9722c3d3-d3a1-431e-b74f-7c157c9f230a%2F29408845-fe59-4025-bd98-f874bab4714a%2Fxqz4y7f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b
(a) Determine the magnetic flux density inside of a very long solenoid (b, n₂, 1) using
Ampere's law.
(b) Now assume that a short solenoid (a, n, l) lies inside of this long solenoid.
Calculate the mutual inductance of these two solenoids.
![Question 6
We have proved that the mutual inductance of coil 1 due to coil 2 are equal to the
mutual inductance of coil 2 due to coil 1 (L₁2 = L21 = M). In a complicated situation
(like this problem) that calculating the flux of one coil linking to the other coil (₁2) is
difficult, we can instead calculate the 21 and then calculate the mutual
conductance.
a
b
1
The figure shows a short solenoid (with length 1, radius a, and n1 turns per unit
length) lies on the axis of a very long solenoid (with radius b, and
n2 turns per unit
length). The short solenoid carries current I. We would like to determine the mutual
inductance of these two coils [Since the inner solenoid is short, it has a very
complicated field, and it puts a different amount of flux through each turn of the
long solenoid.]. Instead we can assume that the current I is flowing through the wire
of the long solenoid and it is inducing on short solenoid. To find the mutual
inductance M, do these two steps:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9722c3d3-d3a1-431e-b74f-7c157c9f230a%2F29408845-fe59-4025-bd98-f874bab4714a%2F8st7587_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 6
We have proved that the mutual inductance of coil 1 due to coil 2 are equal to the
mutual inductance of coil 2 due to coil 1 (L₁2 = L21 = M). In a complicated situation
(like this problem) that calculating the flux of one coil linking to the other coil (₁2) is
difficult, we can instead calculate the 21 and then calculate the mutual
conductance.
a
b
1
The figure shows a short solenoid (with length 1, radius a, and n1 turns per unit
length) lies on the axis of a very long solenoid (with radius b, and
n2 turns per unit
length). The short solenoid carries current I. We would like to determine the mutual
inductance of these two coils [Since the inner solenoid is short, it has a very
complicated field, and it puts a different amount of flux through each turn of the
long solenoid.]. Instead we can assume that the current I is flowing through the wire
of the long solenoid and it is inducing on short solenoid. To find the mutual
inductance M, do these two steps:
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