A thin conducting strip of width h = 2.0 cm is tightly wound in the shape of a very long coil with cross-section radius R = 2.5 cm to make a single-layer straight solenoid. A direct current I = 5.0 A flows through the strip. Find the magnetic induction inside and outside the solenoid as a function of the distance r from its axis.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. In the case, current is flowing in two mutual perpendicular directions.
(1) A part of current I 1 is flowing along the length of solenoid. Due to this current, the system behaves as a hollow long tube of radius R.
The magnetic field due to long hollow tube is
B 1 = 0 at r < R B 2 = 
at r > R
(2) Remaining part of current is flowing along the circumference of the coil. Due to this, the system behaves as a long solenoid.
The magnetic field due to this is B 2 = µ 0 nI 2 (where r < R)
Here n = 
(number of turns per unit length)
∴ B 2 = 
I 2 (when r < R)
Here I 2 = I 
∴ B 2 = 
I 
when r > R, B 2 = 0 Hence, at r < R
= 
+ 
∴ B = 
I 
At r > R 
= 
+ 
∴ B = 
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