Question

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

Answer 1

Explanation:

Step 1:

Given data in the question  

wire radius  r = 0.5 mm

Width of any turn, = wire diameter, 2r = 1 mm = $1 \times 10^{-3} \mathrm{m}$

∴ Total number of solenoid turns in 1 m

$n=\frac{1}{1 \times 10^{-3}}=10^{3}$

Step 2:

Current Magnitude   i = 5 A

Using this equation    $B=\mu_{0} n i$

Put the given values in above equation  

Step 3:

Then we get

$B=4 \pi \times 10^{-7} \times 10^{3} \times 5$

$B=20 \pi \times 10^{-7} \times 10^{3}$

$B=20 \pi \times 10^{-4}$

$B=20 \times 3.14 \times 10^{-4}$

$B=62.8 \times 10^{-4}$

$B=6.28 \times 10^{-3} T$

Answer 2

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Above answer is correct