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Well it is according to faraday's laws of electromagnetic induction. Whenever a coil rotates in a magnetic field,magnetic flux passing through the coil will get changed, and faradays first law states that whenever there is a change in magnetic flux linked with the coil, a emf is induced in it. So due to this emf bulb will light up. Well if you want the change in flux to be explained in more general way I can explain it like this: Suppose it is raining and you have kept a bucket to accumulate the rain water in it. Initially keep the bucket vertical, so maximum amount of rain water will drop into bucket. Now start tilting the bucket, the waterdrops entering the bucket will start decreasing. now make the bucket horizontal, so now no drop will enter into the bucket. So number of water drops entering the bucket depends on inclination of bucket. Here rainddrop is similar to magnetic flux and bucket is similar to coil. So as you rotate the coil, flux linked with the coil changes.

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