Solve number 1, 2, and 3. (2) Induced electromotive force produced by mutual ind

Question

Solve number 1, 2, and 3.

(2) Induced electromotive force produced by mutual induction In this experiment a secondary coil with the sectional area A2 and the number of turns N2 is placed inside a primary coil with length I1 and the number of toms .V,. In addition the induced electromotive force e is produced in the secondary coil due to the alternative current I = I o sin (wt - phi)carried by the primary col. The magnetic field Ilia density inside the primary coil treating as a solenoid is given by = where is the magnetic permeability in vacuum The magnetic field flux produced by the primary coil passing though the secondary coil is given by now the electromotive force in the secondary coil from Faraday's law of induction is given by In the experiment actually measured values we the effective values of the alternative current and the induced electromotive force. Since the effective values of the alternative current and the induced electromotive force are respectively, the quantities are related by the following formula

Explanation / Answer

1)

We know that

The magnetic field inside a solenoid is B =uoni

The magnetic flux through each turn

@ =BA =uoniA

The net magntic flux linked with all the tunsin the solenoid is =uoniA*nl

The self inductance of the solenoid is Li= total flux linked with the coil

L =uon2Al

Now intermsof total number of turns N of the solenoid is

L =uoN2A/l

2)

The magnetic flux througheach primary coil is @ =BA =uon1ia/l

Since the secondary is wound closely over the central the central position of primary and heance the same flux is also linked witheach turn of the secondary

The total magnetic flux linked with secondary is =uon1a*a*n2/l

If M be the mutual inductance of the two coils, the total flux linked with the seconday is Mi

Mi =uon1ian2/l

M =uon1n2a/l Where l is the length of the coil

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