Two air-cored solenoids are designed to have the exact same self-inductance. The first solenoid has one-fourth the length of the second solenoid, while their cross-sectional areas are identical. The ratio of the total

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Quantrex Academy · Accepted Answer

Correct answer: A. 1:2

The self-inductance of a solenoid in terms of total number of turns

N

is given by

L = \dfrac{\mu_0 N^2 A}{l}

.

Since both solenoids are air-cored and have the same self-inductance (

L_1 = L_2

) and identical cross-sectional areas (

A_1 = A_2

), we have:

\dfrac{N_1^2}{l_1} = \dfrac{N_2^2}{l_2}

\Rightarrow \left(\dfrac{N_1}{N_2}\right)^2 = \dfrac{l_1}{l_2}

Given that

l_1 = \dfrac{l_2}{4}

, we get

\dfrac{l_1}{l_2} = \dfrac{1}{4}

.

\Rightarrow \dfrac{N_1}{N_2} = \sqrt{\dfrac{1}{4}} = \dfrac{1}{2}

Thus, the ratio of the total number of turns is

1:2

.

Answer:

1:2

Two air-cored solenoids are designed to have the exact same...

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