A 159-turn solenoid with a length of 20 cm and radius of 0.6 cm carries a curren

Question

A 159-turn solenoid with a length of 20 cm
and radius of 0.6 cm carries a current of 2.2 A.
A second coil of 4 turns is wrapped tightly
about this solenoid so that it can be consid-
ered to have the same radius as the solenoid.
Find the change in the magnetic flux
through the coil when the current in the
solenoid increases to 4 A in a period of
0.7 s. The permeability of a vacuum is 4 pi × 10-7 T · m/A
Answer in units of T · m2.

012 (part 2 of 2) 10.0 points
Find the magnitude of the average induced
emf in the coil.
Answer in units of µV.

Explanation / Answer

number of turns of solenoid   N1 = 159 turns length of solenoid   L = 20 cm = 0.2 m radius of solenoid   r = 0.6 cm = 0.006 m number of turns of coil N2 = 4   magnetic field in side the solenoid is              B = o N1 I / L    magnetic flux through the coil is             =  N2 B A                = ( o N1 N2 A / L) ( I )           d = ( o N1 N2 A / L) ( I )                 = (4*10-7 )(159)(4) (*0.0062 ) ( I2 - I1 ) / 0.2                 = 8.135*10-7 T m 2      magnitude of the average induced emf in the coil.           = d / dt               = (8.135*10-7 ) / 0.7               = 1.1621 V

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