Question

why do the leaves of a gold leaf electroscope diverge when a charged body is brought in contact with its disc do they always diverge to the same extent

Answer 1

The leaves of an electroscope diverge because when an object is touched on the metal disc, the charge travels through the metal rod to the leaves. Since LIKE charges repel, the charge travels till the leaves and the open up as both the leaves have like chargeS

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Answer 2

When a charged body is brought in contact with the disc of a gold-leaf electroscope then, some of the excess charges of the body go in the disc of the electroscope. And then through the metal rod the charged also approach to the gold leaves and the gold leaves get charged. And as we know that there is repulsion between same type of charge so, the leaves of a gold-leaf electroscope diverge when a charged body is brought in contact with its disc.

No, the leaves of the gold-leaf electroscope do not always diverge to the same extent. The divergence between the leaves depends on the amount of charge that is brought in contact with the disc of the electroscope. If the charge will be more then the divergence will be more and if the charge will be less then the divergence will be also less.