Two air core solenoids have the same lengdth of 80 cm and same cross-sectional area `5cm^(2).` Find the mutual inductance between them if the number of turns in the first coil is 1200 turns and that in the second coil is 400 turns.

Explanation

Given : Length of the solenoids `l=80cm`
`=80xx10^(-2)m`
Area of the solenoids `A=5cm2=5xx10^(-4)m^(2)`
No. of turns in the first coil `N_(1)=1200`
No of turns in the second coil `N_(2)=400`
To find :
Mutual inductance between them M = ?
`M=mun_(1)n_(2)A_(2)l`
Formula :
`n_(1)=(N_(1))/(l)`
`n_(2)=(N_(2))/(l)`
`A_(1)=A_(1)=A`
`mu=mu_(0)mu_(r)=mu_(0)=4pixx10^(-7)m`
Solution :
`4pixx10^(-7)xx(1200)/(80xx10^(-2))xx(400)/(80xx10^(-2))xx5xx10^(-4)xx80xx10^(-2)`
M = 0.38H