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Q.

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 the solenoid as a function of the distance $r$ from its axis.

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a

$B_{1} = 0 a t r < R$

b

$B_{2} = \frac{μ_{0} I}{2 π r} a t r > R$

c

None

d

Both $(1) a n d (2)$

answer is C.

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Detailed Solution

In the case, current is flowing in two mutual perpendicular directions.

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
$B_{1} = 0 a t r < R$
$B_{2} = \frac{μ_{0} I}{2 π r} a t r > R$

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