A conical solenoid!

Electricity and Magnetism Level 5

You take a cone and wrap a thin wire around its curved surface, such that there are $n$ turns per unit slant height. The half angle of cone is $\theta = 45^{\circ}$ . The wire carries a current $I$ . If the value of magnetic field created at the center of base is $B_{0} \mu T$ , find $\lfloor B_{0} \rfloor$

Details

$\mu_{0} = 4 \pi \times 10^{-7}, I = 20, n = 5$ (All quantities given in the appropriate SI units)

The answer is 55.

1 solution

Anish Puthuraya
Feb 1, 2014

Using the diagram (which I required a lot of time to make),

$\displaystyle dB = \frac{\mu_o i(\frac{x}{\sqrt{2}})^2}{2((\frac{x}{\sqrt{2}})^2 + (\ell-\frac{x}{\sqrt{2}})^2)^{\frac{3}{2}}} n dx$

Integrating from $0$ to $\sqrt{2}\ell$ ,

$\displaystyle B = \frac{\mu_o ni}{4} ln(\frac{\sqrt{2}+1}{\sqrt{2}-1})$

Substituting the values,
$B = 55.3 \mu T$

$\Rightarrow\lfloor B_o\rfloor = \boxed{55}$

The link doesnt seem to work. Here it is:
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Anish Puthuraya - 7 years, 4 months ago

How do you integrate it? I was stuck for a long time and then used wolfram..

Ashiqul Islam - 6 years ago

How does it matter? Generally, Physics matters. Thats why nowadays, All the physists are great coders too!! They code their own program for their own question :D

Md Zuhair - 2 years, 10 months ago

A conical solenoid!

The answer is 55.

1 solution

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