Let us consider two solenoids A and B, made from same magnetic material of relative permeability μr and equa

Question

Let us consider two solenoids A and B, made from same magnetic material of relative permeability \(\mu_{r}\) and equal area of cross-section. Length of A is twice that of B and the number of turns per unit length in A is half that of B. The ratio of self inductances of the two solenoids, \(L_{A}: L_{B}\) is

(1) 1: 2

(2) 2: 1

(3) 8: 1

(4) 1: 8

Answer 1

Correct option is : (1) 1 : 2

\(L=\mu_{0} \mu_{r} \times n \times A \times N\)

\(L=\mu_{0} \mu_{r} n \times A \times \frac{N}{l} \times l\)

\(L=\mu_ 0 \mu_{r} \times n^{2} \times A \times l \)

\(\Rightarrow L \propto n^{2} l\)

\(\Rightarrow \frac{L_{A}}{L_{B}}=\frac{n_{A}^{2}}{n_{B}^{2}} \times \frac{l_{A}}{l_{B}}\) 

\(\Rightarrow \frac{L_{A}}{L_{B}}=\frac{1}{4} \times 2=\frac{1}{2}\)