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Chapter 23: Problem 10

A solid conducting slab is inserted between the plates of a capacitor, not touching either plate. Does the capacitance increase, decrease, or remain the same?

Short Answer

Expert verified
The capacitance will increase, approaching infinity.

Step by step solution

01

Understanding the definition of capacitance

In an electrical circuit, capacitance is the amount of charge that a capacitor can store for a given electric potential difference across its plates. Mathematically, it is expressed as \( C = \frac{Q}{V} \), where \(Q\) is the charge and \(V\) is the voltage or electric potential difference.
02

Understand how dielectric affects capacitance

When a dielectric (insulating material) is inserted between the plates of a capacitor, it increases the capacitance of the capacitor as it allows the capacitor to store more charge for the same electric potential difference. This happens because dielectric material tends to reduce the electric field between the plates, which effectively reduces the voltage \(V\), thus causing an increase in \(C\).
03

Consider the action of a conducting slab

In our case, the slab is a conductor, not a dielectric. A conductor inserted between the plates of the capacitor will change the situation. Within a conductor, the electric field is zero. Consequently, the potential difference \(V\) across the conductor will also be zero. This will make the capacitance approach infinity, as \(C = \frac{Q}{0}\), and division by zero yields infinity in mathematics.

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