Difference between charge and charge density

In summary, the conversation is discussing the calculation of charge and charge density on a perfectly conducting sphere. The question is specifically asking for the surface charge density, which is the amount of charge per unit area on the surface of the sphere. This is different from the total charge, Q, which is the amount of charge in the entire sphere. The formula for surface charge density is q/A, where q is the charge and A is the area of the sphere. The question is asking for the charge in a small shell on the surface of the sphere and not the electric field.
  • #1
vysero
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So I am studying Gauss's law and I am a bit confused about something. If I am asked to compute the volume or surface charge density of a solid perfectly conducing sphere with a charge Q and radius r, what is being asked of me? Am I just being asked to compute the volume of a sphere and multiply it by Q? I am not sure. Here is what I would do:

E = Q/(4(pi)(epsilon)(r^2) therefore Q = E/4(pi)(epsilon)(r^2)

Is this correct or is there a difference between charge Q and charge density?
 
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  • #2
As far as I understand what you are asking they are asking you to calculate charge density on a sphere in terms of Q and r. your awnser ought not to have anything to do with the electric field.
Much like mass density, charge density is the amount of charge/space The surface charge density is defined as amount of charge per unit area of the surface.
The question is how much charge is in a little shell on the surface between radius r and r+dr per unit area.
in other words: ##\frac{q_{surface}}{A_{sphere}}##. Think for a second: what would happen to a bunch of charges inside of a conducting sphere considering that like charges repel. How much of that charge would be on the surface?
 

1. What is the difference between charge and charge density?

Charge refers to the fundamental property of matter that causes it to experience electrical and magnetic interactions. It is measured in units of coulombs (C). Charge density, on the other hand, refers to the amount of charge per unit volume or area. It is measured in units of coulombs per cubic meter (C/m3) or coulombs per square meter (C/m2).

2. How are charge and charge density related?

Charge density is directly proportional to charge. This means that as the amount of charge increases, the charge density also increases. However, the charge density also depends on the size of the object or area in which the charge is distributed. A larger object or area with the same amount of charge will have a lower charge density compared to a smaller object or area.

3. What is the significance of charge and charge density in physics?

Charge and charge density play a crucial role in determining the behavior of matter in the presence of electric and magnetic fields. They are fundamental concepts in the study of electromagnetism and are used to explain various phenomena such as electric currents, electric fields, and magnetic fields.

4. Can charge and charge density be negative?

Yes, both charge and charge density can be negative. In the case of charge, a negative charge indicates an excess of electrons, while a positive charge indicates a deficiency of electrons. Similarly, a negative charge density means there is an excess of negative charge in a given volume or area, while a positive charge density means there is a deficiency of negative charge.

5. How is charge density measured?

Charge density is typically measured using a device called an electrometer, which can measure the amount of charge present on an object or in a given volume or area. It can also be calculated by dividing the total charge by the volume or area in which it is distributed.

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