Gauss's Law and charged conductors

In summary, in electrostatic equilibrium, the charge on the outer surface of a conductor is 0. This is because the net charge on the conductor is already accounted for by the point charge -Q inside and the inner surface of the conductor. Therefore, there is no excess charge to distribute on the outer surface.
  • #1
veevee
7
0
A conductor carries a net charge +Q. There is a hollow cavity inside the conductor that contains a point charge -Q. In electrostatic equilibrium,what is the charge on the outer surface of the conductor?

A. -2Q
B. -Q
C. 0
D. Q
E. 2Q


I know that the answer is 0, however, I cannot understand why. i would think that the inner surface of the conductor is +Q to offset the -Q point charge inside, which would make the outer surface +Q in order to account for the net +Q charge. However, that is not the case.

Can some one please offer me some help understanding this problem?Thanks so much
 
Physics news on Phys.org
  • #2
If the charge on the inner surface of the conductor is +Q, and the net charge on the conductor is also +Q, how much charge is left over to distribute on the outer surface?
 
  • #3
Oh ok, I see. It's 0. For some reason i thought that the +Q and the -Q would cancel out.
 

1. What is Gauss's Law and how is it used in studying charged conductors?

Gauss's Law is a fundamental principle in electromagnetism that describes the relationship between electric charges and electric fields. It states that the electric flux through any closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space. This law is used to calculate the electric field around a charged conductor, which is important in understanding the behavior of charged particles in conductors.

2. How does Gauss's Law apply to conductors with different shapes and sizes?

Gauss's Law states that the electric field on the surface of a conductor is always perpendicular to the surface and has a magnitude that is directly proportional to the surface charge density. This means that the shape and size of a conductor do not affect the electric field on its surface, as long as the charge density remains constant. This makes Gauss's Law a powerful tool for analyzing the behavior of charged conductors of any shape or size.

3. Can Gauss's Law be used to calculate the electric field inside a charged conductor?

No, Gauss's Law only applies to the electric field outside of a charged conductor. Inside a conductor, the electric field is always zero because the charges are in a state of equilibrium and there is no net movement of charge. Any excess charge on the surface of the conductor will reside on the outer surface, leaving the interior electric field free.

4. How does the presence of other charges or insulators affect the electric field on a charged conductor?

Gauss's Law applies to any closed surface, whether it is a conductor or an insulator. If there are other charges or insulators nearby, they will contribute to the total electric flux through the surface and therefore affect the electric field on the conductor. Additionally, if the conductor is not isolated, meaning it is connected to other conductors or a power source, the presence of other charges will also affect the distribution of charge on the surface of the conductor.

5. Can Gauss's Law be used to calculate the electric potential on a charged conductor?

Yes, Gauss's Law can be used to determine the electric potential on a charged conductor. By integrating the electric field over a path from a reference point to a point on the conductor's surface, we can calculate the potential difference between these two points. This is known as the voltage and it is directly proportional to the charge on the conductor and inversely proportional to the permittivity of free space.

Similar threads

Electric field external to Conducting Hollow Sphere with charge inside
    • Introductory Physics Homework Help
Replies
17
Views
400
Gauss' law and Faraday cage problem
    • Introductory Physics Homework Help
Replies
10
Views
733
Sheet of charge - theory
    • Introductory Physics Homework Help
Replies
1
Views
65
Concept of electric field and hollow conductors
    • Introductory Physics Homework Help
Replies
13
Views
1K
Charge on inner/outer surfaces of two large parallel conducting plates
    • Introductory Physics Homework Help
Replies
11
Views
392
I Thought I Understood Gauss' Law (Sheets)
    • Introductory Physics Homework Help
Replies
26
Views
576
Gauss' law -- Conductor with a cavity
    • Introductory Physics Homework Help
Replies
4
Views
893
Several questions relating to work, electric potential energy, and potential difference
    • Introductory Physics Homework Help
Replies
22
Views
1K
Electric field sphere calculations with a hollow cavity using Gauss' law
    • Introductory Physics Homework Help
Replies
21
Views
2K
What is the charge on the outer surface of the middle conductor?
    • Introductory Physics Homework Help
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top