Question

12. The length of a solenoid is 20 cm. Its area of cross
section is 10 cm2, and the number of turns is
1000. Another coil of 500 turns is wound in the
middle. Their coefficient of mutual induction will be
nearest to
(1)π/2 ×10^-4H
(2) 10πx 10^-4H
(3) 2π x 10^-4H
(4) π^2 x 10^-4H​

Answer 1

$\Large\underline{\underline{\sf Given:}}$

• Lenght of solenoid (l) = 20cm

• Area (A) = 10cm² or $\sf{10×10^{-4}m^2}$

• Number of turns in first coil $\sf{N_1}$ = 1000

• Number of turns in second coil $\sf{N_2}$=500

$\Large\underline{\underline{\sf To\:Find:}}$

• Coefficient of mutual induction(M)

$\Large\underline{\underline{\sf Formula\:Used:}}$

$\large{\boxed{\boxed{\sf \pink{M=\dfrac{\mu_oN_1N_2A}{l}}}}}$

$\Large\underline{\underline{\sf Solution:}}$

$\implies{\sf M=\dfrac{4π×10^{-7}×1000×500×10×10^{-4}}{0.2} }$

$\implies{\sf M=\dfrac{2π×10^7×10^{-11}}{0.2} }$

$\implies{\sf \red{M=10π×10^{-4} \: H}}$

$\Large\underline{\underline{\sf Answer:}}$

Option (2)

Coefficient of mutual induction will be ${\bf M=10π×10^{-4} \: H}$

Answer 2

Answer:

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