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JEE Main 202131 AugustMorning Shift
Exam
JEE Main
Year
2021
Date
31 August
Shift
Morning Shift
Subject
Physics
Chapter
Magnetic Effects of Current

JEE Main 2021 · 31 August · Morning Shift · Physics · Magnetic Effects of Current

A coil having N turns is wound tightly in the form of a spiral with...

A coil having NN turns is wound tightly in the form of a spiral with inner and outer radii aa and bb respectively. Find the magnetic field at centre, when a current II passes through coil :A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. Find

Options

  1. Aμ0I8[a+ba−b]\dfrac{{\mu}_{0}I}{8}\left[\dfrac{a + b}{a - b}\right]
  2. Bμ0I4(a−b)[1a−1b]\dfrac{{\mu}_{0}I}{4 ( a - b )}\left[\dfrac{1}{a} - \dfrac{1}{b}\right]
  3. Cμ0I8(a−ba+b)\dfrac{{\mu}_{0}I}{8}\left(\dfrac{a - b}{a + b}\right)
  4. Dμ0IN2(b−a)log⁡e(ba)\dfrac{{\mu}_{0}IN}{2 ( b - a )}\log_{e}\left(\dfrac{b}{a}\right)

Correct answer

D. μ0IN2(b−a)log⁡e(ba)\dfrac{{\mu}_{0}IN}{2 ( b - a )}\log_{e}\left(\dfrac{b}{a}\right)

Step-by-step solution

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. Find
Recall the formula of the magnitude of the magnetic field in terms of current and permeability in free space, B=∫abμ0dNi2x=∫abμ0(Nb−adx)i2x=μ0Ni2(b−a)ln⁡(ba)B = {∫}_{a}^{b}\dfrac{{\mu}_{0}dNi}{2x} = {∫}_{a}^{b}\dfrac{{\mu}_{0}\left(\dfrac{N}{b - a}dx\right)i}{2x} = \dfrac{{\mu}_{0}Ni}{2 ( b - a )}\ln \left(\dfrac{b}{a}\right).
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