Answered: 1. Solenoid: The magnetic field inside… | bartleby

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symmetries.
1. Solenoid: The magnetic field inside a very long solenoid must be along the axis
of the solenoid. The magnetic field outside the solenoid is approximately zero.
A very long solenoid of radius b carries a current I with turns per length. We
want to use Ampere's law to find the magnetic field at a point P a distance ?
from the central axis. Assume r<b so point P is inside the solenoid.
a. To take advantage of the symmetry, we choose the Amperian loop to be a
rectangle. The rectangle must extend outside the solenoid to enclose
current. We need to introduce a height H to make a closed loop but H must
not be in the final answer. We will calculate $5 ds at one leg at a time.
i. What is the integral 5 ds along the left leg of the Amperian loop, i.e.,
outside the solenoid?
ii. What is the integral 5 ds along the top and bottom
horizontal legs of the Amperian loop? Hint: think about
the angle between 8 and ds along these legs.
iii. What is the integral - ds along the right leg of the
Amperian loop, i.e., inside the solenoid? Answer in
terms of the unknown 8 and H, b and/or 7.
b. What is the current going through the rectangle? Answer in
terms of I, n, H, b and/or r.
B & 0
H
I (out)
0000000
B
Use your results above and apply Ampere's law to find the magnetic field inside the solenoid.
Holl
********.
E
BR 0
n tums
per
length
7 (in)

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