Consider the following statements about a solenoid: 1. The magnetic

Consider the following statements about a solenoid:

  • 1. The magnetic field strength in a solenoid depends upon the number of turns per unit length in the solenoid
  • 2. The magnetic field strength in a solenoid depends upon the current flowing in the wire of the solenoid
  • 3. The magnetic field strength in a solenoid depends upon the diameter of the solenoid

Which of the statements given above are correct ?

1, 2 and 3
1 and 3 only
2 and 3 only
1 and 2 only
This question was previously asked in
UPSC NDA-1 – 2019
Statements 1 and 2 are correct.
The magnetic field strength inside a long solenoid is given by the formula B ≈ μ₀ * n * I, where μ₀ is the permeability of free space, n is the number of turns per unit length (n = N/L), and I is the current flowing through the solenoid.
Statement 1 is correct as B is directly proportional to n (number of turns per unit length).
Statement 2 is correct as B is directly proportional to I (current).
Statement 3 is incorrect. For an ideal long solenoid, the magnetic field strength inside the solenoid (away from the ends) does not depend on its diameter. While the diameter might have minor effects in non-ideal cases (finite length solenoid, field near ends), the standard formula and theoretical treatment indicate no dependence on diameter for the uniform field inside a long solenoid.
The formula B = μ₀nI is an approximation that holds well for solenoids whose length is much greater than their diameter. In such cases, the magnetic field is strong, uniform inside (except near the ends), and zero outside.
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