NEET Class neet Answered
In fig 6.6 , angle θ between direction of area S and magnetic field B is greater than 90 .
If θ > 90 , then flux Φ is negative . when magnitude of magnetic field decreasing , magnitude of flux is also decreasing.
Hence when magnetic field decreasing , flux changes from more negative to less negative .
Hence (dΦ/dt) is positive . ( But in the explanation given for fig 6.6 , it is mentioned that (dΦ/dt) is negative. This is error)
Hence if (dΦ/dt) is positive , then induced current is negative .
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Another prescription of determining the direction of induced current is described below
As shown in above figures , let us consider observer is viewing the coil.
The direction of area vector S of coil is always from coil to observer as shown in above figures.
If direction of magnetic field B is towards the observer , then direction of magnetic field makes acute angle θ ( θ < 90 )
with direction of area vector as shown in fig.1.
If direction of magnetic field B is away from observer , then direction of magnetic field makes obtuse angle θ ( θ > 90 )
with direction of area vector as shown in fig.2.
Faraday's law of induction states that induced EMF ε is proportional to change of flux Φ with respect to time .
where is flux of magnetic field .
Hence induced EMF is
................................(1)
If induced EMF ε is positive , then induced current is also poitive.
By convention, positive induced current flows counterclockwise direction in the coil when viewd from observer.
If induced EMF ε is negative , then induced current is also negative .
By convention, negative induced current flows clockwise direction in the coil when viewed from observer .
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In Fig.(1) , if magnetic field is increasing dB/dt is positive , θ is acute and cosθ is positive.
From eqn.(1) , induced EMF ε is negative and induced current also negative .
Hence induced current flows in clockwise direction.
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In Fig.(1) , if magnetic field is decreasing dB/dt is negative , θ is acute and cosθ is positive.
From eqn.(1) , induced EMF ε is positive and induced current also positive .
Hence induced current flows in counterclockwise direction.
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In Fig.(2) , if magnetic field is increasing dB/dt is positive , θ is obtuse and cosθ is negative.
From eqn.(1) , induced EMF ε is positive and induced current also positive .
Hence induced current flows in counterclockwise direction.
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In Fig.(2) , if magnetic field is decreasing dB/dt is negative , θ is obtuse and cosθ is negative.
From eqn.(1) , induced EMF ε is negative and induced current also negative .
Hence induced current flows in clockwise direction.
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If we apply the same procedure to the given figure 6.6 in question , we see for the second case when magnetic field
is decreasing and it makes obtuse angle , then induced current is in negative direction ( clockwise direction )