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A current-carrying circular loop having n number of turns per unit length has a current I through it. If the current through it and the number of turns per unit length are doubled, then the magnetic field at the centre of the loop will:

A current-carrying circular loop having n number of turns per unit length has a current I through it. If the current through it and the number of turns per unit length are doubled, then the magnetic field at the centre of the loop will: Correct Answer Increase by four times

The correct answer is Increase by four times.

  • A circular loop of wire is a solenoid. 
  • The magnetic field strength inside a solenoid is given by:
  • B = μ0nI (inside a solenoid) where
    • n is the number of loops per unit length of the solenoid,
    • I is the current flowing,
    • μ0 is known as the magnetic constant or the permeability of free space.
    • Further, n = N/l, with N being the number of loops and l the length.
  • It is given that the current flowing and the number of turns per unit length are doubled, it means that the magnetic field strength becomes four times.
  • To simplify it further, since B = μ0nI before the change in a number of turns and current.
    • When n => 2n and I => 2I,
    • The equation becomes μ0(2n)(2I).
  • Hence, B becomes 4B after a double increase in the number of turns and the current flowing through it.

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