# Determine the magnitude of the charge on the inner and outter surface of sphere

• gothloli
In summary, a hollow conducting spherical shell with inner radius of 8 cm and outer radius of 10 cm has an electric field of 90 N/C at the inner surface and 80 N/C at the outer surface. Using Gauss's law, the charge on the inner surface and outer surface can be determined by setting up Gaussian surfaces and considering the potential at different distances from the center. By symmetry, the isolated charge inside the shell can be considered at the center, with additional charges spread on the inside and outside surfaces. The total potential can be written by adding up the potential from all three charges.
gothloli

## Homework Statement

A hollow conducting spherical shell has an inner radius of 8 cm and an outer radius of
10 cm. The electric field at the inner surface of the shell, Ei, has a magnitude of 90 N/C
and points toward the centre of the sphere, and the electric field at the outer surface, Eo,
has a magnitude of 80 N/C and points away from the center of the sphere (see Figure A).
Determine the magnitude of the charge on the inner surface and the outer surface of the
spherical shell.

## Homework Equations

For the inner surface: E =kqt/r1r^{3}
For the outer surface E = kqt/r2^{2}

## The Attempt at a Solution

This uses Gauss's law. For the inner surface, set gaussian surface, with r1<r, r is the inner radius.
For outer surface, gaussian surface outside the sphere. r2>rs which is radius of shell.
I'm stupid I don't know what to do.

For there to be a field inside the conducting shell, there must be some isolated charge inside it. By symmetry, you can consider that to be at the centre. Let that charge be qc. There are also charges spread over the inside surface of the sphere, qi say, and on the outside surface, qo.
Can you write down an expression for the potential at distance r from the centre? To start with, just consider a single shell of charge at some radius a. You need to consider r < a and r > a separately. When you've got that, you can write down the total potential from the three charges just by adding them up.

## 1. What is the definition of magnitude in regards to charge?

Magnitude refers to the strength or amount of a charge. It is typically measured in coulombs (C) in the SI system.

## 2. How is the charge on the inner and outer surface of a sphere related?

The charge on the inner and outer surface of a sphere is equal in magnitude but opposite in sign. This is because the charge on the inner surface induces an equal and opposite charge on the outer surface.

## 3. How can the magnitude of the charge on a sphere be determined?

The magnitude of the charge on a sphere can be determined by using Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

## 4. What factors can affect the magnitude of the charge on a sphere?

The magnitude of the charge on a sphere can be affected by the material of the sphere, the charge of the object inducing the charge, and the distance between the two objects.

## 5. How does the charge on a sphere impact its electric field?

The charge on a sphere creates an electric field around it, with the direction of the field lines pointing away from the positively charged inner surface and towards the negatively charged outer surface.

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