A solenoid of length 0.5 m has a radius of 1 cm and is made up of 'm' number of turns. It carries a current of 5 A. If the magnitude of the magnetic field inside the solenoid is 6.28 × 10⁻³ T then the value of m is __________.

Solution

Physics sir · 4 steps

Inside a long solenoid only turns per metre matter, so the 1 cm radius is a decoy.

1. Field inside. Inside a long solenoid the field is uniform and depends only on the turns per unit length n = m/L and the current. The radius does not appear anywhere.

   B = μ₀ n I = μ₀ m/L I ⇒ m = (B L)/(μ₀ I)

2. Denominator first. μ₀ I = 4π × 10⁻⁷ × 5 = 20π × 10⁻⁷ = 6.28 × 10⁻⁶ T m.
3. Put in numbers. m = (6.28 × 10⁻³ × 0.5)/(6.28 × 10⁻⁶) = 0.5 × 10³. The 6.28 cancels neatly.
4. So. The solenoid has 500 turns.

The common slip: 1000. Treating m as the turns per metre, that is using B = μ₀ m I without dividing by L = 0.5 m, gives 1000 instead of 500.

The idea to keep. For a long solenoid, B = μ₀ n I with n in turns per metre. Always divide total turns by length, and ignore the radius.

Answer from the NTA final answer key. Solution by PrepWiser.