Each plate of a parallel plate capacitor has a charge q on it. The capacitor is now connected to a battery .Now,a) The facing surfaces of the capacitor have equal and opposite charges.b) The two plates of the capacitor have equal and opposite charges.c) The battery supplies equal and opposite charges to the two plates. d) The outer surfaces of the plates have equal charges.

This is a question from H C Verma .

When we analyze a parallel plate capacitor connected to a battery, it's essential to understand how charge distribution works. Let's break down the statements regarding the charges on the capacitor plates and the role of the battery.

Understanding Charge Distribution in a Capacitor

A parallel plate capacitor consists of two conductive plates separated by an insulating material (dielectric). When the capacitor is charged, one plate accumulates a positive charge while the other plate accumulates an equal amount of negative charge. This creates an electric field between the plates.

Examining Each Statement

• Facing surfaces of the capacitor have equal and opposite charges: This statement is true. The facing surfaces of the plates are where the electric field is generated, and they must have equal and opposite charges to maintain the electric field between them.
• The two plates of the capacitor have equal and opposite charges: This is also correct. If one plate has a charge of +q, the other must have a charge of -q. This balance is crucial for the capacitor's function.
• The battery supplies equal and opposite charges to the two plates: This statement is accurate as well. When the capacitor is connected to a battery, the battery forces electrons to move from one plate to the other, resulting in one plate becoming positively charged and the other negatively charged.
• The outer surfaces of the plates have equal charges: This statement is generally false. The outer surfaces of the plates do not necessarily have equal charges because the charge distribution can vary depending on the surrounding environment and the presence of other conductive objects. The inner surfaces facing each other are what maintain the equal and opposite charge condition.

Visualizing the Concept

Imagine a water tank with two compartments separated by a barrier. When you fill one compartment with water (representing positive charge), the other compartment will have an equal amount of water displaced (representing negative charge). The barrier ensures that the water levels (charges) are balanced, similar to how the plates in a capacitor work.

Role of the Battery

The battery acts as a pump that moves charge. When connected, it pushes electrons from one plate to the other, establishing the necessary charge difference. This process continues until the capacitor reaches its maximum charge capacity, defined by the voltage of the battery and the capacitance of the capacitor.

Summary of Key Points

In summary, when a parallel plate capacitor is connected to a battery:

• The facing surfaces of the plates have equal and opposite charges.
• The two plates themselves have equal and opposite charges.
• The battery supplies equal and opposite charges to the plates.
• The outer surfaces of the plates do not necessarily have equal charges.

This understanding of charge distribution is fundamental in grasping how capacitors function in electrical circuits. It highlights the importance of both the physical structure of the capacitor and the role of external power sources like batteries.