The number of turns a coil wrapped around the outside of the solenoid should have is : 127 turns
Given data :
Diameter of solenoid = 25-cm
Rate of increase of magnetic field = 2.4 T/s
Induced emf = 15 v
Induced emf = N ( dФ / dt ) ---- ( 1 )
where : ( dФ / dt ) = ( A (db/dt) )
Equation ( 1 ) becomes
Induced emf = N A ( db/dt ) ------ (2)
From equation ( 2 )
N = Induced emf / A ( db/dt ) ------ ( 3 )
where : Induced emf = 15 v . db/dt = 2.4 T/s , A = area of solenoid
Area of solenoid = πr² = π * ( 0.125 )²
Insert values into equation ( 3 )
N = 15 / ( π * ( 0.125 )² ) * 2.4
= 127.32 ≈ 127 turns
Hence we can conclude that The number of turns a coil wrapped around the outside of the solenoid should have is : 127 turns.
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Below is the missing part of the question
The magnetic field inside a 25-cm-diameter solenoid is increasing at 2.4 T/s
