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A 200 turn coil of radius 2 cm is placed...

A 200 turn coil of radius 2 cm is placed coil axially within a long solenoid of 3 cm radius. If the turns density of the solenoid is 90 turns per cm, then calculate mutual inductance of the coil.

Text Solution

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Number of turns of the solenoid `N_(2)=200`
Radius of the solenoid, r=2cm `=2 x 10^(-2)m`
Area of the solenoid, `A=pi r^(2)=3.14 xx (2 xx 10^(-2))^(2=1.256 xx 10^(-3) m^(2)`
Turn density of long solenoid per cm, `N_(1)=90 xx 10^(2)`
Mutual inductance of the coil, `M=(mu_(0)N_(1)N_(2)A)/(l)=(4pi xx 10^(-7) x 90 xx 10^(2) xx 200 xx 1.256 xx 10^(-3))/(1)`
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