Moving Charges and Magnetism Problems - Numerical 11

Two solenoids P and Q have length and the total number of turns in the ratio of 1:2. What is the ratio of the magnetic field inside the two solenoids due to the same current?

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Suggested solution:

Suggested solution:

Let N₁ and L₁ denote the total number of turns and length of the solenoid P. The corresponding quantities for the solenoid Q are N₂ and L₂.

Given:

Let n₁ and n₂ denote the number of turns per unit length in the solenoid P and Q respectively, Obviously

Since n and I are same, B will be same. Therefore B₁ / B₂ = 1