Two air-cored solenoids, P and Q , are constructed using insulated copper wire. Solenoid P has a total of N turns, a radius of 2r , and a length L . Solenoid Q has a total of 3N turns, a radius of r , and a length 3L .

Question

Quantrex Academy · Accepted Answer

Correct answer: A. 4 : 3

The self-inductance of a solenoid is given by

L_{self} = \dfrac{\mu_0 N^2 A}{l}

, where

N

is the total number of turns,

A

is the cross-sectional area, and

l

is the length.

For solenoid

P

:

N_P = N

A_P = \pi (2r)^2 = 4\pi r^2

l_P = L

L_P = \dfrac{\mu_0 N^2 (4\pi r^2)}{L} = \dfrac{4\mu_0 N^2 \pi r^2}{L}

For solenoid

Q

:

N_Q = 3N

A_Q = \pi r^2

l_Q = 3L

L_Q = \dfrac{\mu_0 (3N)^2 (\pi r^2)}{3L} = \dfrac{9\mu_0 N^2 \pi r^2}{3L} = \dfrac{3\mu_0 N^2 \pi r^2}{L}

The ratio of their self-inductances is:

\dfrac{L_P}{L_Q} = \dfrac{4}{3}

Answer:

4 : 3

Two air-cored solenoids, P and Q , are constructed using insulated...

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