- #1
Titan97
Gold Member
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Homework Statement
A thin insulated wire forms a plane spiral of N turns carrying a current ##i##. The inner radius is ##b## an outer radius is ##a##. Find magnetic field at centre of spiral
Homework Equations
$$B=\frac{n\mu_0i}{2R}$$
The Attempt at a Solution
For an area of ##\pi(b^2-a^2)##, number of turns is N.
So for an elemental area of ##2\pi r dr##,number of turns ##n## is ##\frac{2rNdr}{(b^2-a^2)}##
After substing ##n##, $$dB=\frac{\mu_0 I 2Ndr}{2(b^2-a^2)}$$
But on integrating, I am getting wrong answer
Instead of taking number of turns per unit area, if I took number turns per unit width, I got the correct answer. That is if $$n=\frac{N}{b-a}$$.
Why does the answer change?