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22/01/2022 2:10 pm
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A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil
(1) \(\frac{μ_0IN}{2(b - a)}log_e\)\(\Big(\frac{b}{a}\Big)\)
(2) \(\frac{μ_0I}{8}\)\(\Big[\frac{a+b}{a-b}\Big]\)
(3) \(\frac{μ_0I}{4(a-b)}\)\(\Big[\frac{1}{a} - \frac{1}{b}\Big]\)
(4) \(\frac{μ_0I}{8}\)\(\Big(\frac{a-b}{a+b}\Big)\)
1 Answer
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22/01/2022 2:15 pm
Correct answer: (1) \(\frac{μ_0IN}{2(b - a)}log_e\)\(\Big(\frac{b}{a}\Big)\)
Explanation:
No. of turns in dx width = \(\frac{N}{b-a}\)dx
∫dB = \(\int_a^b \Big(\frac{N}{b-a}\Big)\)dx \(\frac{μ_0i}{2x}\)
B = \(\frac{μ_0IN}{2(b - a)}\ell n\)\(\Big(\frac{b}{a}\Big)\)