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  • (a) Explain the meaning of the term mutual inductance. Consider two concentric circular coils, one of the radius r1 and the other of radius r2 <img alt="\left ( r_{1}< r_{2} \right )" src="https://entrancecorner.codecogs.com/gi

(a) Explain the meaning of the term mutual inductance. Consider two concentric circular coils, one of the radius r1 and the other of radius r2 \left ( r_{1}< r_{2} \right ) placed coaxially with centres coinciding with each other. Obtain the expression for the mutual inductance of the arrangement.
(b) A rectangular coil of area A, having number of turns N is rotated at 'f' revolutions per second in a uniform magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2 \pif NBA.

 

 

 

 
 
 
 
 

Answers (1)

Mutual inductance is the property of pair of coils due to which an emf is induced in one coil due to change in current in another coil
given r_{1}< r_{2}
magnetic field due to coil with radius r2
B_{2}= \frac{\mu_{0}I_{2}}{2r_{2}}
Magnetic flux linked with coil c1
\phi _{12}= B_{2}\pi r_{1}^{2}= \frac{\mu_{0}I_{2}}{2r_{2}}\times \pi r_{1}^{2}---(i)
if M is the mutual inductance of two coils
\phi _{12}=MI_{2}---(2)
from (1) & (2)
M= \frac{\mu_{0}\pi r_{1}^{2}}{2r_{2}}
b) magnetic flux associated with l each turns of coil

\phi = BA\cos w t
emf induced

=\frac{ -Nd\phi }{dt}
=-NBA\frac{d}{dt}\cos wt
=NBAw\sin wt
Maximum induced emf
e=NBAw
w=2\pi f
e=2\pi fNBA

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Safeer PP

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