Introduction:
When a plastic rod is rubbed with wool, it acquires a negative charge due to the transfer of electrons from wool to the rod. This negatively charged plastic rod when brought near the knob of a negatively charged gold leaf electroscope causes the gold leaf to dilate.

Reasons for dilation of gold leaf:
The dilation of gold leaf in a negatively charged gold leaf electroscope can be explained by the following reasons:

1. Repulsion of like charges:
The knob of a negatively charged gold leaf electroscope contains an excess of negative charges. When a negatively charged plastic rod is brought near the knob, the like charges on the knob and the rod repel each other. This repulsion causes the negative charges in the knob to move away from the rod. As a result, the negative charges in the gold leaf become more concentrated, causing the gold leaf to dilate.

2. Induction:
The negatively charged plastic rod also induces a negative charge on the gold leaf electroscope. This is because the negative charges in the rod repel the electrons in the metal of the electroscope, causing the electrons to move away from the rod and towards the other end of the electroscope. This movement of electrons produces a separation of charges in the electroscope, with the top of the electroscope becoming positively charged and the bottom becoming negatively charged. The negative charge induced on the gold leaf causes it to be repelled by the negative charge on the rod, causing the gold leaf to dilate.

Conclusion:
In summary, the dilation of the gold leaf in a negatively charged gold leaf electroscope when a plastic rod rubbed with wool is brought near the knob can be explained by the repulsion of like charges and the induction of a negative charge on the electroscope.

When a plastic rod is rubbed with wool, the plastic rod acquires negative charge and the wool acquires positive charge due to transfer of electrons from wool to the rod. When this rubbed wool having negative charge is brought near the knob of a negatively charged gold leaf electroscope the negative charge on leaves increases and the leaves having same charge repel each other and spread and the gold leaf dilates.