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The ratio of magnetic field and magnetic moment at the centre of a current carrying circular loop is x. When both the current and radius is doubled the ratio will be
  • a)
    x/8
  • b)
    x/4
  • c)
    x/2
  • d)
    2x
Correct answer is option 'A'. Can you explain this answer?
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The ratio of magnetic field and magnetic moment at the centre of a cur...
Explanation:

  • Let's consider a circular loop of radius 'r' and current 'I' flowing through it.

  • At the centre of the loop, magnetic field is given by the formula B = μ₀I/2r where μ₀ is the permeability of free space.

  • Magnetic moment of the loop is given by the formula M = πr²I, which is the product of current, area and number of turns.

  • The ratio of magnetic field and magnetic moment at the centre of the loop is x = B/M = (μ₀I/2r)/(πr²I) = μ₀/2πr.

  • Now, if we double the current and radius, new magnetic field at the centre of the loop will be B' = μ₀(2I)/(2(2r)) = μ₀I/2r.

  • Similarly, new magnetic moment of the loop will be M' = π(2r)²(2I) = 4πr²I.

  • Hence, the new ratio of magnetic field and magnetic moment at the centre of the loop will be x' = B'/M' = (μ₀I/2r)/(4πr²I) = μ₀/8πr.

  • Therefore, the ratio of magnetic field and magnetic moment at the centre of the loop is reduced to x/8 when both the current and radius are doubled.


Answer: Option A (x/8)
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The ratio of magnetic field and magnetic moment at the centre of a cur...
Magnetic momemt is directly proportional to current and area
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The ratio of magnetic field and magnetic moment at the centre of a current carrying circular loop is x. When both the current and radius is doubled the ratio will bea)x/8b)x/4c)x/2d)2xCorrect answer is option 'A'. Can you explain this answer?
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