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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, 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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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.
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:
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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