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Question

A long solenoid is fabricated by closely winding a wire of radius 0.5 mm over a cylindrical non-magnetic frame such that the successive turns nearly touch each other. What would be the magnetic field B at the center of the solenoid if it carries a current of 5 A ?

A
3.5π×103 T
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B
2π×103 T
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C
5π×103 T
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D
π×103 T
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Solution

The correct option is B 2π×103 T
Let the successive turns of solenoid touch each other as shown in figure.

Width of each turn = diameter d of wire

width of each turn =d=2r=1 mm

Width of each turn =1×103 m

Thus, the number of turns per unit length of solenoid will be

n=1 md=1 m1×103 m=1000

current in solenoid is i=5 A

Using formula, B=μ0ni

B=4π×107×1000×5=20π×104

B=2π×103 T

Hence, option (b) is the correct answer.

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