The value of magnetic field at the centre of a circular loop is ___________.

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OSSC Excise SI (Mains) Official Paper (Held On: 17 Oct, 2024 Shift 2)
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  1. \(\mu_0 \frac{I}{R^2}\)
  2. \(\mu_0 \frac{I}{4}R\)
  3. \(\mu_0 \frac{I}{2}R\)
  4. \(2 \mu_0 \frac{I}{R^2}\)

Answer (Detailed Solution Below)

Option 3 : \(\mu_0 \frac{I}{2}R\)

Detailed Solution

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The correct answer is option 3

Key Points

  • The formula for the magnetic field at the center of a circular loop is B = (μ₀I)/(2R).
  • This formula is derived from the Biot-Savart law.
  • Where μ₀ is the permeability of free space, I is the current, and R is the radius of the loop.
  • The magnetic field is directly proportional to the current and inversely proportional to the radius.

Important Points

  • The magnetic field at the center of a circular loop is uniform and directed perpendicular to the plane of the loop.
  • The direction of the magnetic field follows the right-hand rule.
  • Increasing the current or decreasing the radius will increase the magnitude of the magnetic field.
  • This formula is essential for understanding magnetic fields in circular loops, which is a fundamental concept in electromagnetism.
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