Total interior and exterior charge of a hollow sphere?

In summary, the problem involves a hollow conducting sphere with a point charge placed at the center and an inner radius of R and outer radius of 1.5R. The question asks for the total charge on the interior and exterior walls of the sphere. To solve this, Gauss's Law and the equation σ = Qenc/A can be used. However, the problem does not specifically ask for charge density and instead focuses on the comparison of charges on the inner and outer surfaces of the sphere, as well as the effect of these charges on the electric field outside the sphere.
  • #1
KoontzyN
3
0

Homework Statement


A hollow conducting sphere has inner radius R and outer radius 1.5R. A +40nC point charge is placed at the center. What is the total charge on the interior and exterior walls of the sphere?

R=10cm

Homework Equations


Gauss's Law
σ = Qenc/A

The Attempt at a Solution


I'm not too sure where to start. I know Gauss's Law for a sphere is E=Qenc/4πε0r2 , but I don't know where to go from here.

I also know that to find the charge density σ = Qenc/A. Plugging in the knowns I get σ= 3.18*10^-7 C/m^2. I'm not sure if that relates to the problem at all. Any help is appreciated.

 
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  • #2
You are not asked for charge density.

How does the charge on the outer surface compare with that on the inner surface?
Consider the field outside the sphere. How is that affected by the charges on the sphere?
 

FAQ: Total interior and exterior charge of a hollow sphere?

What is the total interior charge of a hollow sphere?

The total interior charge of a hollow sphere is always zero. This is because the electric field inside a conductor is zero, and a hollow sphere is a type of conductor.

How is the exterior charge of a hollow sphere calculated?

The exterior charge of a hollow sphere can be calculated using the formula Q = 4πε0R, where Q is the total charge, ε0 is the permittivity of free space, and R is the radius of the sphere.

What is the significance of the total charge of a hollow sphere?

The total charge of a hollow sphere determines its electric potential, which describes the amount of work needed to move a unit charge from one point to another within the sphere. It also affects the electric field both inside and outside the sphere.

Can the total charge of a hollow sphere be negative?

No, the total charge of a hollow sphere cannot be negative. This is because a hollow sphere is a neutral object, meaning it has equal amounts of positive and negative charges that cancel each other out, resulting in a total charge of zero.

How is the total charge of a hollow sphere affected by the material it is made of?

The total charge of a hollow sphere is not affected by the material it is made of, as long as the material is a good conductor. This is because the electric field inside a conductor is zero, regardless of the material it is made of.

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