A 200 turn solenoid with a length of 20 cmand a radius of 1.0 cm carries a curre

Question

A 200 turn solenoid with a length of 20 cmand a radius of 1.0 cm carries a currentof 2.0 A. A second coil of four turns iswrapped tightly about this solenoid so that it can be considered tohave the same radius as the solenoid. Find the following when thecurrent in the solenoid increases to 6.0 Ain a period of 0.90 s. (a) the change in the magnetic flux through thecoil
1T·m2
(b) the magnitude of the average induced emf in the coil
2 V

(Please provide a step by step solution. Thanks!)
(a) the change in the magnetic flux through thecoil
1T·m2
(b) the magnitude of the average induced emf in the coil
2 V

(Please provide a step by step solution. Thanks!)

Explanation / Answer

given number of turns N = 200 length of the solenoid l = 0.2m radius of the solenoid r = 0.01m initial current in the loop I1 = 2.0A final current in the loop I2 = 6.0A time required for the increase in current t =0.90s 0 = 4*10-7 Tm/A a) the magnitude of magnetic field inside a solenoid is      B =0NI/l           =(--------)I           =(-------)(I2-I1) here the angle between magnetic field & the plane of theloop is = 00 the change in magnetic flux through the coil is B = (B)Acos            ={B*r2cos}            = ------------- b) number of turns N = 4 the average induced emf in the coil is         =N*B/t            = ------------            = ------------            

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