A 66-mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diam

Question

A 66-mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter. A coil is tightly wound around the solenoid at its center. The coil resistance is 7.7 ohms. The mutual inductance of the coil and solenoid is 34 µH. At a given instant, the current in the solenoid is 810 mA, and is decreasing at the rate of 2.5 A/s.

A) The number of turns in the winding of the solenoid is?
B) At the given instant, the induced emf in the solenoid is?
C) At the given instant, the magnetic energy of the solenoid, in

Explanation / Answer

inductance of a solenoid L = 66*10-3 H length of the solenoid l = 0.80 m diameter of solenoid d = 0.10 m radius of the solenoid r = 0.05 m Area of the solenoid A = r2                                    = (3.14)(0.05)2                                    = 0.00785 m2 Resistance in the coil R = 7.7 ohm current in the solenoid I = 810 *10-3 Amps Mutual inductance M=34*10-6H (a)Formulae for selfinductance L=0N2A/l Solve for N=Ll/0A                    =(66*10-3H)(0.80 m)/(4*10-7 A/m)(0.00785 m2) Number of turns= 2314 ----------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------- (b) Induced emf =L((dI/dt))                         = (66*10-3 H))(2.5A/s)                         = 165 x 10-3v --------------------------------------------------------------------------------------------------------- (c) Magnetic energy stored U=1/2LI2    =1/2(66x10-3 H)(810 x10-3 Amps )2     = 0.021615J -----------------------------------------------------------------------------------------     = 0.021615J ----------------------------------------------------------------------------------------- (d) Induced current in the loop Iloop = /R                                                     = ( 165 *10-3 v )/(7.7 ohms)                                                     = 21.42 mA                                                   

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