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Please clarify the illustration is right or wrong , in diagram they given induced current in clockwise only, or also area vector S in same direction in both , please tell the illustration is wrong or rule they given is wrong
Asked by bharathrocky0017 | 12 Mar, 2024, 09:17: PM

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.

-------------------------------

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.

-------------------------------------------------------------------

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 )

Answered by Thiyagarajan K | 13 Mar, 2024, 08:57: AM

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