An electroscope is based on the principle of electrostatic induction. Here's how it works:

1. Neutral State: A neutral electroscope has two thin metal leaves that hang vertically, connected to a metal rod.

2. Induction: When a charged object is brought near the electroscope, it induces a separation of charges within the metal rod and leaves. This is because the charged object repels like charges and attracts opposite charges in the electroscope.

3. Leaf Divergence: The like charges (either positive or negative) that are repelled to the leaves cause them to spread apart. The greater the charge on the object, the greater the separation of the leaves.

In essence, the electroscope uses the force of repulsion between like charges to indicate the presence and relative magnitude of an electric charge.