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Chapter 23: Problem 7

A capacitor is said to carry a charge \(Q .\) What's the net charge on the entire capacitor?

Short Answer

Expert verified
The net charge on the entire capacitor is 0.

Step by step solution

01

Understanding the Principle of Capacitance

A capacitor is a device that stores electric charge. It's made up of two plates with opposite charges - one plate carries a positive charge, and the other carries an equivalent negative charge.
02

Applying the Principle

Given in the problem that a capacitor carries a charge \(Q\). This means one plate has a charge of \(+Q\) and the other has a charge of \(-Q\). Let's add these two charges.
03

Calculating Net Charge

The net charge of a capacitor is calculated by adding up the charges on both plates. So the net charge \(Q_{net} = +Q + (-Q) = 0\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electric Charge
Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It is quantified in units of Coulombs (C). An object can have a positive, negative, or neutral charge.
  • Positive charge: An excess of protons compared to electrons.
  • Negative charge: An excess of electrons compared to protons.
  • Neutral charge: Equal number of protons and electrons.
Atoms normally have no net charge because they contain an equal number of protons and electrons. When these balances are disturbed, and an object becomes charged, we can use devices like capacitors to store and manage these charges.
Capacitor Plates
A capacitor consists of two conductive surfaces, known as plates, that store electric charges upon the application of a voltage. These plates are separated by an insulator or dielectric material.
  • The surface area and distance between the plates affect the capacitance, or the ability to store charge.
  • Dielectric material increases a capacitor鈥檚 ability to store charge.
The role of the plates in a capacitor is crucial because they provide the space where charges accumulate. One plate accumulates a positive charge, while the other gathers an equivalent negative charge, allowing the capacitor to store energy effectively.
Net Charge
Net charge refers to the total charge of a system. For capacitors, this is the sum of the charges on both plates. In a capacitor, even though each plate may have a large charge, the net charge is often zero.
  • One plate has a charge of "+Q".
  • The other has a charge of "-Q".
  • When combined, these equal and opposite charges sum to zero: \[ Q_{net} = +Q + (-Q) = 0 \].
This neutrality of net charge is key for the capacitor's ability to store energy without releasing net electric charge into the external circuit.
Electric Field
An electric field is a vector field around a charged object that represents the force exerted on other charges within the field. The strength of this field is dependent on the magnitude of the charge and the distance from the charge.
  • Electric fields direct positive charges away and negative charges towards the charged object generating the field.
  • The field between the plates of a capacitor is uniform and directed from the positive to the negative plate.
The electric field in a capacitor stores energy and facilitates the movement of charge when needed, playing a critical role in the device's operation.

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Most popular questions from this chapter

An unknown capacitor \(C\) is connected in series with a \(3.0-\mu \mathrm{F}\) capacitor; this pair is placed in parallel with a 1.0 - \(\mu\) F capacitor, and the entire combination is put in series with a \(2.0-\mu \mathrm{F}\) capacitor. (a) Make a circuit diagram of this network. (b) When a potential difference of \(100 \mathrm{V}\) is applied across the open ends of the network, the total energy stored in all the capacitors is \(5.8 \mathrm{mJ} .\) Find \(C\).

A capacitor's plates hold \(1.3 \mu \mathrm{C}\) when charged to \(60 \mathrm{V}\). What's its capacitance?

A car battery stores about \(4 \mathrm{ M J }\) of energy. If this energy were used to create a uniform \(30-\mathrm{kV} / \mathrm{m}\) electric field, what volume would it occupy?

A solid sphere contains a uniform volume charge density. What fraction of the total electrostatic energy of this configuration is contained within the sphere?

An uncharged capacitor has parallel plates \(5.0 \mathrm{cm}\) on a side, spaced \(1.2 \mathrm{mm}\) apart. (a) How much work is required to transfer \(7.2 \mu \mathrm{C}\) from one plate to the other? (b) How much work is required to transfer an additional \(7.2 \mu \mathrm{C} ?\)
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