Negative charge -Q is distributed uniformly over the surface...

Negative charge $-Q$ is distributed uniformly over the surface of a thin spherical insulating shell with radius $R$. Calculate the force (magnitude and direction) that the shell exerts on a positive point charge $q$ located (a) a distance $r>R$ from the centre of the shell (outside the shell) and (b) a distance $r<R$ from the centre of the shell (inside the shell).

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Key Concepts

Coulomb's Law

Coulomb's Law states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is used to calculate the interaction force between the electric field produced by a charge distribution and another point charge, once the field has been determined.

Electric Field of a Spherical Shell

For a spherical shell with charge uniformly distributed over its surface, the electric field outside the shell is equivalent to that of a point charge located at the center of the shell, while the electric field inside the shell is zero. This property is a direct consequence of the spherical symmetry and simplifies the calculations when dealing with forces on other charges.

Gauss's Law

Gauss's Law relates the electric flux through a closed surface to the enclosed charge. It is particularly powerful for problems with high symmetry, such as spherical symmetry, because it allows for the determination of the electric field in and around a charge distribution by choosing appropriate Gaussian surfaces.

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