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In a gold leaf electroscope, the degree of divergence of gold leafs is an indicator of:

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Hint :Gold leaf electroscope is used to detect, measure and find the nature of a charge. The device is used for detecting electric charge and can also identify its polarity, if compared with a known charge.

Complete Step By Step Answer:
In a gold leaf electroscope, the degree of divergence of gold leafs is an indicator of an amount of charge transferred to the gold leafs through any external source.
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Principle of working of a gold leaf electroscope:
Gold leaf electroscope is a device used for detecting an electric charge and identifying its polarity. It is based on the principle of charge repulsion and electrostatic induction. Electrostatic inductions is the phenomenon of temporary electrification of a conductor in which opposite charges appear at its closer end and similar charges appear at its farther end.
It is also based on a gold leaf electroscope consisting of a vertical conducting rod passing through a rubber stopper fitted in the mouth of a glass vessel. Two thin gold leafs are attached to the lower end of the rod. When a charged object touches the metal knob at the outer end of the rod, the charge flows down to the leaves. The leaves diverge due to the repulsion of charges they have received. The degree of divergence of leaves gives the measure of the amount of charges.
Electroscopes can show the relative charge of an object through the movement of the gold leaves inside. As the gold leaves gain more positive or negative charge, they spread out. To demonstrate this, place a charged object near the electroscope. The object can be something as simple as a polythene rod that has been rubbed with a cloth. By moving the charge near the electroscope’s top plate, it acquires the opposite charge of the object. The closer the object is brought, the greater the separation will be seen inside.

Note :
By touching the top plate of the electroscope with a charged object, the charge is itself transferred to the electroscope. This results in the gold leaves having the same charge and therefore being repelled from each other. When the object is removed, the electroscope will continue to hold the charge.